Multiple choice general knowledge math & puzzles

The joint probability of events A and B is 32 percent with the probability of event A being 60 percent and the probability of event B being 50 percent. Based on this information, the conditional probability of event A given event B has occurred is closest to:

  1. 30.0%.

  2. 53.3%

  3. 64.0%

  4. 16.0%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The conditional probability formula states P(A|B) = P(A ∩ B) / P(B). Given P(A ∩ B) = 0.32 and P(B) = 0.50, we calculate P(A|B) = 0.32 / 0.50 = 0.64 = 64%. This means there's a 64% chance that event A occurs when we know event B has occurred. Option D would be the joint probability P(A ∩ B), not the conditional probability.

AI explanation

To find the conditional probability of event A given event B has occurred, we can use the formula for conditional probability:

[ P(A|B) = \frac{P(A \cap B)}{P(B)} ]

Given that the joint probability of events A and B is 32%, we have ( P(A \cap B) = 32\% = 0.32 ).

Given that the probability of event A is 60%, we have ( P(A) = 60\% = 0.60 ).

Given that the probability of event B is 50%, we have ( P(B) = 50\% = 0.50 ).

Substituting these values into the formula for conditional probability, we have:

[ P(A|B) = \frac{0.32}{0.50} \approx 0.64 ]

Therefore, the conditional probability of event A given event B has occurred is closest to 64.0%. Hence, the correct answer is option C.

Keep practicing — related questions