If A, B and C are three independent events such that P(A)=P(B)=P(C)=P then P (at least two of A, B, C occur )=

Question

If A, B and C are three independent events such that P(A)=P(B)=P(C)=P then P (at least two of A, B, C occur )= (A) P 3-3 P (B) 3 P-2 P2 (C) 3 P2-2 P3 (D) 3 P 2

Tardigrade Admin · Accepted Answer

P(A)=P(B)=P(C)=P P(A) ⋅ P(B) ⋅ P(C)+3 ⋅ P2(1-p) P3+3 p2(1-P)=3 P2-2 P3

Q. If $A, B$ and $C$ are three independent events such that $P (A) = P (B) = P (C) = P$ then $P$ (at least two of $A, B, C$ occur $) =$

$P^{3} - 3 P$

$3 P - 2 P^{2}$

$3 P^{2} - 2 P^{3}$

$3 P^{2}$

$P (A) = P (B) = P (C) = P$
$P (A) \cdot P (B) \cdot P (C) + 3 \cdot P^{2} (1 - p)$
$P^{3} + 3 p^{2} (1 - P) = 3 P^{2} - 2 P^{3}$

Q. If A,B and C are three independent events such that P(A)=P(B)=P(C)=P then P (at least two of A,B,C occur )=

P3−3P

3P−2P2

3P2−2P3

3P2