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

Step-by-step solution

Probability to show 3 or 5 is array ll & p= 2 6 = 1 3 & q=1- 1 3 = 2 3 & P(X 2) array aligned & = ^4 C ₂ ( 1 3 )^2 ( 2 3 )^2+ ^4 C ₃ ( 1 3 )^3 ( 2 3 )^1+ ^4 C ₄ ( 1 3 )^4 ( 2 3 )^0 & =6 ( 1 9 ) ( 4 9 )+4 ( 1 27 ) ( 2 3 )+1 ( 1 81 ) & = 24+8+1 81 & = 33 81 = 11 27 aligned Four fair dice are thrown independently 27 times. Expected number =27 11 27 =11