Question

If a1, a2, . . . , an are independent events with probabilities p1, p2, . . . , pn respectively, then

Answer 1

Answer:

Concept used:

Two events A and B are said to be independent if

P(A∩B)=P(A).P(B)

similarly $A_1,A_2,.......A_n$ are said to be independent if

P($A_1$∩$A_2$∩......$A_n$)$=P(A_1).P(A_2)........P(A_n)$

Given:

$P(A_1)=p_1$

$P(A_2)=p_2$

.

.

$P(A_n)=p_n$

since $A_1,A_2,.......A_n$ are independent,

P($A_1$∩$A_2$∩......$A_n$)$=P(A_1).P(A_2)........P(A_n)$

P($A_1$∩$A_2$∩......$A_n$)$=p_1.p_2.p_3...........p_n$