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ISI2016-MMA-10

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If $A_1, A_2, \dots , A_n$ are independent events with probabilities $p_1, p_2, \dots , p_n$ respectively, then $P( \cup_{i=1}^n A_i)$ equals

  1. $\Sigma_{i=1}^n \: \: p_i$
  2. $\Pi_{i=1}^n \: \: p_i$
  3. $\Pi_{i=1}^n \: \: (1-p_i)$
  4. $1-\Pi_{i=1}^n \: \: (1-p_i)$

1 Answer

2 2 votes

Consider value of n as 2,

We know

P(A1 U A2) = P(A1) + P(A2) - P(A1nA2)

=p1 + p2 -  p1p2 (Ai are Independent Events)

=p1(1-p2) + p2

=p1(1-p2)+p2+1-1 (Adding and Subtracting 1)

=p1(1-p2)-(1-p2)+1

= 1+(1-p2)(p1-1)

= 1-(1-p1)(1-p2)

Answer : D

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