Question

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.
Which of the following is the conditional probability of A, given B?

A. 5/6
B. 1/5
C. 1/6
D. The answer cannot be determined from the information given

Answer 1

Answer:

(C) 1/6

Step-by-step explanation:

Pr that event A will occur = 0.5

Pr that event B will occur = 0.6

Pr that both A and B occurs = 0.1

Pr(A) = 0.5

Pr(B)= 0.6

Pr(AnB) = 0.1

The conditional probability of A given B is Pr (A|B) = Pr(AnB) / Pr(A)

= 0.1/0.6

= 1/6 (C)

Answer 2

The conditional probability of A, given B is $P(A|B)=\dfrac{1}{6}$

The Probability of occurring event A is $0.5$

The Probability of occurring event B is $0.6$

The Probability of occurring both events A and B is $0.1$.

Substitute the value of the parameters $P(A\cap B)$ and $P(B)$ in the formula $P(A|B)=\dfrac{P(A\cap B}{P(B)}$ to get the conditional probabilty of A, given B as-

$\begin{aligned}P(A|B)&=\dfrac{P(A\cap B}{P(B)}\\P(A|B)&=\dfrac{P(0.1}{0.6}\\P(A|B)&=\dfrac{1}{6}\end{aligned}$

So, the conditional probability of A, given B is $P(A|B)=\dfrac{1}{6}$

Learn more about conditional probability here:

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