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Let {A} ,{B} ,{C} be three events. If the probability of occur

Question

Let $A$ , $B$ , $C$ be three events. If the probability of occurring exactly one event out of $A$ and $B$ is $1 - x$ , out of $B$ and $C$ is $1 - 2 x$ , out of $C$ and $A$ is $1 - x$ and that of occurring three events simultaneously is $x^{2}$ , then prove that the probability that at least one out of $A$ , $B$ , $C$ will occur is greater than 1/2 .

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Elizabeth Discussed

Let

A

B

C

be three events. If the probability of occurring exactly one event out of

A

and

B

1 - x

, out of

B

and

C

1 - 2 x

, out of

C

and

A

1 - x

and that of occurring three events simultaneously is

x^{2}

, then prove that the probability that at least one out of

A

B

C

will occur is greater than 1/2 .

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Question Text

Let

A

B

C

be three events. If the probability of occurring exactly one event out of

A

and

B

1 - x

, out of

B

and

C

1 - 2 x

, out of

C

and

A

1 - x

and that of occurring three events simultaneously is

x^{2}

, then prove that the probability that at least one out of

A

B

C

will occur is greater than 1/2 .

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