Question

two cards are drawn successively with replacement from a pack of 52 cards. Find the probability distribution of the number of diamonds and the mean of the distribution. Select the correct answer from above options

Answer 1

There are `13` diamonds in a pack of `52` cards. So, probability when both drawn cards are not diamond, `P(D =0) = (52-13)/52**(52-13)/52 = 39/52*39/52 = 9/16` Probabilty of drawing `1` diamond in any of the draw, `P(D =1) = (13/52**39/52)+(39/52**13/52) = 3/8` Probabilty of drawing `2` diamonds, `P(D =2) = (13/52**13/52) = 1/16` Now, mean of the given distribution can be given as, `M = sum_(i=1)^n P_ix_i` `M = 0*9/16+1*3/8+2*1/16 = 3/8+1/8 = 1/2` So, mean of the distribution is `1/2.`