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Question

Statement-I : In throwing of two dice, let the events A, B and C be 'the first dice shows an even number', 'the second dice shows an odd numbers' and 'both the dice show an odd numbers or both the dice show an even number’ respectively. Then $text end text P left parenthesis A right parenthesis equals P left parenthesis B right parenthesis equals P left parenthesis C right parenthesis equals fraction numerator 1 over denominator 2 end fraction text end text$ and $P left parenthesis A intersection B right parenthesis equals P left parenthesis B intersection C right parenthesis equals P left parenthesis C intersection A right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ Therefore A, B and C are mutually independent events
Statement-II : Three events A, B and C are mutually independent if and only if P(A Ç B) = P(A) . P(B), P(B Ç C) = P(B) . P(C), $P left parenthesis C intersection A right parenthesis equals P left parenthesis C right parenthesis$ = P(C) . P(A) and $P left parenthesis A intersection B intersection C right parenthesis$ = P(A) . P(B) . P(C)

Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I
Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
Statement-I is True, Statement-II is False
Statement-I is False, Statement-II is True

The correct answer is: Statement-I is False, Statement-II is True

Related Questions to study

The probability that 4th power of a positive integer ends in the digit 6 is:

The probability that 4th power of a positive integer ends in the digit 6 is:

Let A, B, C be pairwise independent events with P(C)> 0 and $P left parenthesis A intersection B intersection C right parenthesis equals 0$ . Then $P open parentheses A to the power of c end exponent intersection B to the power of c end exponent C close parentheses text is equal to: end text$

Let A, B, C be pairwise independent events with P(C)> 0 and $P left parenthesis A intersection B intersection C right parenthesis equals 0$ . Then $P open parentheses A to the power of c end exponent intersection B to the power of c end exponent C close parentheses text is equal to: end text$

Let A and B be two events such that $P left parenthesis stack A union B with bar on top right parenthesis equals fraction numerator 1 over denominator 6 end fraction comma P left parenthesis A intersection B right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ and $P left parenthesis stack A with bar on top right parenthesis equals fraction numerator 1 over denominator 4 end fraction comma text where end text stack A with bar on top$ stands for complement of event A. Then events A and B are-

Let A and B be two events such that $P left parenthesis stack A union B with bar on top right parenthesis equals fraction numerator 1 over denominator 6 end fraction comma P left parenthesis A intersection B right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ and $P left parenthesis stack A with bar on top right parenthesis equals fraction numerator 1 over denominator 4 end fraction comma text where end text stack A with bar on top$ stands for complement of event A. Then events A and B are-

parallel

A random variable X has the probability distribution :

For the events E = {X is a prime number} and F = {X < 4}, the probability $P left parenthesis E union F right parenthesis$ is-

A random variable X has the probability distribution :

For the events E = {X is a prime number} and F = {X < 4}, the probability $P left parenthesis E union F right parenthesis$ is-

A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.

A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.

An experiment resulting in sample space as S = {a, b, c, d, e, f} $text with end text P left parenthesis A right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis B right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis C right parenthesis equals fraction numerator 2 over denominator 16 end fraction comma P left parenthesis D right parenthesis equals fraction numerator 3 over denominator 16 end fraction comma P left parenthesis e right parenthesis equals fraction numerator 4 over denominator 16 end fraction text and end text P left parenthesis f right parenthesis equals fraction numerator 5 over denominator 16 end fraction text . end text$ Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}. $text If end text P left parenthesis A divided by B right parenthesis equals p subscript 1 end subscript comma P left parenthesis B divided by C right parenthesis equals p subscript 2 end subscript comma P open parentheses C divided by A to the power of c end exponent close parentheses equals p subscript 3 end subscript text and end text P open parentheses A to the power of c end exponent divided by C close parentheses equals p subscript 4 end subscript$ then the correct order sequance is

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parallel

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parallel

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parallel

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parallel

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