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Union of Sets

Let two fair ...

Question

Let two fair six - faced dice A and B be thrown simultaneously. If $E_{1}$ is the event that die A shows up four, $E_{2}$ is the event that die B shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

are independent.

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are independent.

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are independent.

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are independent.

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Solution

The correct option is C
are independent.

$P (E_{1}) = \frac{1}{6} P (E_{2}) = \frac{1}{6} P (E_{1} \cap E_{2}) = P (A shows 4 and B shows 2) = \frac{1}{36} = p (E_{1}) . P (E_{2}) S o, E_{1}, E_{2} are independent A l s o a s E_{1} \cap E_{2} \cap E_{3} = ϕ S o P (E_{1} \cap E_{2} \cap E_{3}) \neq P (E_{1}) . P (E_{2}) . P (E_{3}) S o E_{1}, E_{2}, E_{3}$

are not independent.

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Let two fair six - faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

The correct option is C are independent. P(E1)=16P(E2)=16P(E1∩E2)=P(A shows 4 and B shows 2)=136=p(E1).P(E2)So,E1,E2are independentAlso as E1∩E2∩E3=ϕSo P(E1∩E2∩E3)≠P(E1).P(E2).P(E3)So E1,E2,E3 are not independent.

Let two fair six - faced dice A and B be thrown simultaneously. If $E_{1}$ is the event that die A shows up four, $E_{2}$ is the event that die B shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?