QJEEM20Ma767e: JEE Main 2020 Mathematics - Class 11 JEEM20Ma767e Solution: Four fair dice are thrown independently 27 times. Then the…

4 dice are independently thrown. Each die has probability to show 3 or 5 is

$P = {2 \over 6} = {1 \over 3}$

$\therefore$ $q = 1 - {1 \over 3} = {2 \over 3}$ (not showing 3 or 5)

Experiment is performed with 4 dices independently

$\therefore$ Their binomial distribution is

${(q + p)^4} = {(q)^4} + {}^4{C_1}{q^3}p + {}^4{C_2}{q^2}{p^2} + {}^4{C_3}q{p^3} + {}^4{C_4}{P^4}$

$\therefore$ In one throw of each dice probability of showing 3 or 5 at least twice is

= ${p^4} + {}^4{C_3}q{p^3} + {}^4{C_2}{q^2}{p^2}$

$= {{33} \over {81}}$

Given such experiment performed 27 times

$\therefore$ So expected outcomes = np

= ${{33} \over {81}} \times 27$

= 11