JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q17

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MathematicsSingle correct+4 / -1Question 17 of 90

A six faced die is biased such that

$3\times P(\text{a prime number})=6\times P(\text{a composite number})=2\times P(1)$ .

Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

\dfrac3{11}

\dfrac5{11}

\dfrac7{11}

\dfrac8{11}

Answer and worked solution

Official answer: D

Face probabilities. Each prime face $\frac k3$ , each composite $\frac k6$ , face 1 $\frac k2$ . Then $\frac{11k}6=1$ , so $k=\frac6{11}$ .

Perfect square (1 or 4): $\frac k2+\frac k6=\frac4{11}$ .

Mean for two throws $\frac8{11}$ . (D)

Topics:Random variables and distributions Classical probability

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JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 17