Question

suppose that A and B are independent events. if P(A)=.4 and P(B)=.1, what is P(A∩B¹)? A .54 B .06 C .36 D .04

Answer 1

ANSWER

$P(A \cap B')=0.36$


EXPLANATION

If event A and event B are independent, then

$P(A \cap B)= P(A ) \times P(B)$

otherwise A and B are dependent events.



We were given that,

$P(A) = 0.4$


and

$P(B) = 0.1$


and we were asked to evaluate


$P(A \cap B')$

Since A and B are independent,

$P(A \cap B') = P(A ) \times P(B')$
Recall that,



$P(B') = 1 - P( B)$


This implies that,

$P(A \cap B') = P(A ) \times (1 - P(B) )$


We now substitute the above values to obtain,


$P(A \cap B') = 0.4 \times (1 - 0.1 )$






$P(A \cap B') = 0.4 \times 0.9$


$P(A \cap B') = 0.36$


Therefore the correct answer is C.