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Conditional Probability & Bayes' Theorem · Question 16 of 125

Question 16

MediumOriginal question

P(A)=0.6P(A) = 0.6, P(B)=0.4P(B) = 0.4 and P(A∪B)=0.7P(A \cup B) = 0.7. What is P(A∣B)P(A \mid B)?

Options for question 16

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(A∩B)=0.6+0.4−0.7=0.3P(A \cap B) = 0.6 + 0.4 - 0.7 = 0.3.

  2. P(A∣B)=0.30.4=0.75P(A \mid B) = \frac{0.3}{0.4} = 0.75.

Worth noting

0.5 is P(B∣A)=0.30.6P(B \mid A) = \frac{0.3}{0.6}, dividing by the wrong event.

Concept
Conditional probability from given probabilities
Typical time
90 s
Your time
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The rule this testsConditional probability
Practise this chapter →

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Practise this chapter →

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.