Question

2. a) Let A and B be two events such that P(A) 4, P(B) .5 and P(AnB) 3 Find P(AUB). b) Let A and B be two events such that P(A)-5, P(B) 3 and P(AUB) .6. Find P(An B)

Answer 1

Answer

(A) we know that the formula for $P(A \cup B)$ is given as

$P(A \cup B)$ = P(A) + P(B) - $P(A \cap B)$

we have P(A) = 0.4, P(B) = 0.5 and $P(A \cap B)$ = 0.3

setting the values in the formula, we get

$P(A \cup B)$ = 0.4 + 0.5 - 0.3 = 0.9-0.3 = 0.6

So, required value of $P(A \cup B)$ is 0.6

(B) we know that the formula for $P(A \cap B)$ is given as

$P(A \cap B)$ =P(A)+P(B) - $P(A \cup B)$

it is given that P(A) = 0.5, P(B) =0.3 and $P(A \cup B)$ = 0.6

setting the values in the above formula, we get

$P(A \cap B)$ = 0.5 +0.3 - 0.6 = 0.8 - 0.6 = 0.2

Therefore, $P(A \cap B)$ = 0.2