JEE PYQ: Probability Question 21
Question 21 - 2020 (05 Sep Shift 1)
Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.
Show Answer
Answer: 11
Solution
$P(\text{3 or 5 on a die}) = \frac{2}{6} = \frac{1}{3}$. $P(\text{at least 2}) = 1 - P(0) - P(1) = 1 - \left(\frac{2}{3}\right)^4 - {}^4C_1\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)^3 = 1 - \frac{16}{81} - \frac{32}{81} = \frac{33}{81} = \frac{11}{27}$. $E = 27 \times \frac{11}{27} = 11$.
BETA
