JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q87

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MathematicsSingle correct+4 / -1Question 87 of 90

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 ?

E_1

and

E_2

are independent.

E_2

and

E_3

are independent.

E_1

and

E_3

are independent.

E_1

E_2

and

E_3

are independent.

Answer and worked solution

Official answer: D

$P(E_1)=P(E_2)=\frac16$ and $P(E_3)=\frac12$ . Each pair is independent: $P(E_1E_2)=\frac1{36}$ , $P(E_1E_3)=P(E_2E_3)=\frac3{36}=\frac1{12}$ . But A = 4 and B = 2 make an even sum, so $P(E_1E_2E_3)=0\ne\frac1{72}$ : the three are not independent.

Topics:Independent events

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 87