Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Conditional Probability Practice Quiz Part 1

Test your knowledge with expert conditional probability quiz

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on conditional probability for high school students.

What is the definition of conditional probability?
The probability of event B occurring given that event A has occurred
The probability of event A occurring given that event B has occurred
The probability of event A occurring independently of event B
The total probability of both events A and B occurring
Conditional probability measures the likelihood of event A occurring when it is known that event B has occurred. This concept is central to understanding how additional information impacts probability estimates.
How is conditional probability calculated when P(B) > 0?
P(A|B) = P(A) / P(B)
P(A|B) = P(A) * P(B)
P(A|B) = P(A and B) / P(B)
P(A|B) = P(B) / P(A and B)
The formula for conditional probability is defined as P(A|B) = P(A ∩ B) / P(B) when P(B) is greater than zero. This fundamental definition helps in updating probabilities based on new information.
If events A and B are independent, what is true about their conditional probability P(A|B)?
P(A|B) equals 0
P(A|B) equals P(A)
P(A|B) equals P(B)
P(A|B) equals 1
For independent events, the occurrence of event B does not affect the likelihood of event A. Therefore, the conditional probability P(A|B) remains equal to the unconditional probability P(A).
If P(B) = 0.5 and P(A and B) = 0.2, what is P(A|B)?
0.5
0.25
0.4
0.6
Using the conditional probability formula, P(A|B) is calculated as 0.2 divided by 0.5, which equals 0.4. This straightforward calculation reinforces understanding of the basic formula.
When is it appropriate to use the conditional probability formula?
Only when events have equal probabilities
When the probability of the conditioning event is greater than zero
Only when events are independent
When the events are mutually exclusive
The conditional probability formula is used only when the probability of the conditioning event (P(B)) is greater than zero. This ensures that the division is defined and meaningful.
In a factory, Machine A produces 40% of gadgets with a defect rate of 3% and Machine B produces 60% with a defect rate of 5%. If a gadget is defective, what is the probability it was produced by Machine A?
Approximately 40%
Approximately 60%
Approximately 28.6%
Approximately 12%
By applying Bayes' theorem, the defective rate contributed by Machine A is computed and then divided by the total defect rate, yielding approximately 28.6%. This question demonstrates the use of conditional probability in practical scenarios.
An urn contains 5 white balls and 3 black balls. Two balls are drawn without replacement. What is the probability that the second ball is black given the first ball drawn was white?
3/7
5/8
1/2
3/8
After a white ball is drawn, there are 7 balls left in the urn, 3 of which are black. Thus, the probability of drawing a black ball second is 3/7.
If P(A) = 0.4 and P(B|A) = 0.5, what is the value of P(A and B)?
0.2
0.1
0.7
0.9
The multiplication rule states that P(A and B) equals the product of P(A) and P(B|A). Multiplying 0.4 by 0.5 gives 0.2.
Assume events A and B are mutually exclusive with P(A)=0.3 and P(B)=0.5. What is the conditional probability P(A|A ∪ B)?
0.8
0.5
0.375
0.3
For mutually exclusive events, P(A ∪ B) is the sum of P(A) and P(B), which is 0.8. Therefore, P(A|A ∪ B) is calculated as 0.3 divided by 0.8, resulting in 0.375.
In a deck of 52 cards, what is the probability that a drawn card is a king given that it is a face card?
1/4
1/2
1/3
1/13
There are 12 face cards in a deck and 4 of these are kings. Therefore, the probability that a face card drawn is a king is 4/12, which simplifies to 1/3.
A diagnostic test for a disease is 95% accurate and the disease occurs in 1% of the population. If a person tests positive, what is the probability they actually have the disease?
5%
1%
Approximately 16%
95%
Despite the high accuracy of the test, the low prevalence of the disease means that false positives are significant. Using Bayes' theorem, the actual probability of having the disease given a positive test is approximately 16%.
Suppose 70% of students study for an exam. If the probability of passing given that they study is 0.9, and 0.4 if they do not study, what is the overall probability of passing?
0.7
0.75
0.63
0.9
The overall probability of passing is found by using the law of total probability: (0.7×0.9) + (0.3×0.4) equals 0.75. This combines the probabilities for both studying and not studying.
If 80% of employees are full-time and 15% of full-time employees receive promotions, what is the probability that a randomly selected employee is both full-time and promoted?
0.15
0.12
0.68
0.80
The probability of a full-time employee receiving a promotion is the product of being full-time (0.8) and receiving a promotion (0.15), which equals 0.12. This straightforward multiplication demonstrates joint probability.
If 60% of customers buy a product and 25% of them use a coupon, what is the probability that a customer both buys the product and uses a coupon?
0.60
0.25
0.85
0.15
By multiplying the probability of buying the product (0.60) with the probability of using a coupon (0.25), the joint probability is 0.15. This is a direct application of the multiplication rule.
How does independence between two events affect the calculation of conditional probability?
For independent events, P(A|B) equals P(A and B)
For independent events, P(A|B) equals P(A)
For independent events, P(A|B) equals P(B)
For independent events, P(A|B) is greater than P(A)
Independence implies that the occurrence of one event does not affect the probability of the other. Thus, the conditional probability P(A|B) remains the same as the marginal probability P(A).
In a factory, 30% of parts come from Supplier X with a defect rate of 4%, and 70% from Supplier Y with a defect rate of 7%. If a part is found defective, what is the probability it was supplied by Supplier X?
Approximately 30%
Approximately 70%
Approximately 19.7%
Approximately 40%
By applying Bayes' theorem, the probability of a defective part coming from Supplier X is calculated by weighing the defect contributions from both suppliers. The resulting probability is approximately 19.7%.
In a survey, 40% of students play sports. Among these, 60% participate in clubs. For those who do not play sports, 20% join clubs. If a student is in a club, what is the probability that they play sports?
40%
60%
Approximately 66.7%
20%
Using the law of total probability and Bayes' theorem, the probability that a student who is in a club plays sports is determined to be approximately 66.7%. This involves combining the club participation rates for both groups.
In a hospital, 5% of infants are born with a condition. A test detects the condition correctly 90% of the time and falsely gives a positive 10% of the time for healthy infants. If an infant tests positive, what is the probability they have the condition?
50%
Approximately 32.1%
5%
90%
Even though the test is highly accurate, the low prevalence of the condition means false positives can be significant. Bayes' theorem combines these factors to yield an approximate probability of 32.1% that a positively tested infant truly has the condition.
Given that P(C|A ∩ B) = 0.8, P(C|A' ∩ B) = 0.3, P(A ∩ B) = 0.25, and P(B) = 0.5, what is P(C|B)?
0.80
0.65
0.55
0.45
Using the law of total probability, P(C|B) can be expressed as P(C|A∩B)×P(A|B) + P(C|A'∩B)×P(A'|B). With P(A|B) calculated as 0.25/0.5 = 0.5, the computation yields 0.8×0.5 + 0.3×0.5 = 0.55.
In a population, 30% are smokers. Among smokers, 20% have a respiratory illness, while among non-smokers, 5% have the illness. If a person has the illness, what is the probability they are a smoker?
5%
20%
Approximately 63.2%
30%
Applying Bayes' theorem, the probability is calculated by dividing the likelihood of a smoker having the illness by the overall illness rate. The computation yields an approximate probability of 63.2% that an ill person is a smoker.
0
{"name":"What is the definition of conditional probability?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the definition of conditional probability?, How is conditional probability calculated when P(B) > 0?, If events A and B are independent, what is true about their conditional probability P(A|B)?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the fundamental concepts and definitions of conditional probability.
  2. Analyze probability problems and identify conditional relationships between events.
  3. Apply conditional probability principles to solve engaging and real-world problems.
  4. Evaluate the influence of one event on another using probabilistic reasoning.
  5. Synthesize various probability scenarios to determine overall likelihoods.

Conditional Probability Quiz Part 1 Review Cheat Sheet

  1. Understand conditional probability - It's the chance of an event happening when another event has already occurred, written as P(A|B). The formula P(A|B) = P(A ∩ B)/P(B) shows exactly how knowing B impacts A. Correctly formatted link
    2. GeeksforGeeks
  2. Apply the formula with real-life examples - Turn math into magic by picturing red marbles or card draws! Working through scenarios like "what's the chance of a red marble if green's ruled out?" brings the formula to life. Correctly formatted link
    3. Investopedia
  3. Differentiate from joint probability - Conditional probability asks "given B, what's the chance of A?" while joint probability measures "what's the chance A and B happen together?" It's a subtle but powerful distinction in statistical thinking. Correctly formatted link
    4. GeeksforGeeks
  4. Recognize independent events - When A and B are independent, knowing B gives you zero extra info about A, so P(A|B) = P(A). This concept streamlines many problems where events don't influence each other. Correctly formatted link
    5. GeeksforGeeks
  5. Explore Bayes' Theorem - Bayes' Theorem lets you update your guesses when new evidence arrives: P(A|B) = [P(B|A) × P(A)] / P(B). It's the superstar behind spam filters, medical diagnoses, and even winning game shows! Correctly formatted link
    6. GeeksforGeeks
  6. Practice with word problems - Flex your brain with questions like "What's the chance a student passes science given they already passed math?" Regular drills build that mental muscle and make the concepts stick. Correctly formatted link
    7. Byju's
  7. Understand the multiplication rule - This rule tells you P(A ∩ B) = P(A) × P(B|A), linking intersection and conditional probability. It's a natural extension that ties joint, conditional, and marginal ideas together. Correctly formatted link
    8. GeeksforGeeks
  8. Learn key properties - For example, P(S|A) = 1 because if you know you're in event A, you're definitely in the overall sample space S. Spotting these patterns saves time and avoids pitfalls. Correctly formatted link
    9. GeeksforGeeks
  9. Contrast with marginal probability - Marginal probability ignores any conditions - it's just P(A) on its own. By comparing it to conditional probability, you see how context changes your calculations. Correctly formatted link
    10. Investopedia
  10. Apply to medical testing - Figure out the chance someone has a disease given a positive test result - this real-world twist uses Bayes' Theorem and conditional probability everywhere from hospitals to headlines. It's critical for understanding false positives and true diagnoses! Correctly formatted link
    11. GeeksforGeeks
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker