# problem-5.12

problem-5.12 This is known as de Mere's problem. Although the expected number of successes in each case is identical, as 24/36 = 4/6, the probabilities differ. Namely,

    > 1 - pbinom(0,4,1/6)           # one or more 6 in 4 rolls
    [1] 0.5177
    > 1 - pbinom(0,24,1/36)         # one or more double sixes
    [1] 0.4914

The rolling of four dice is better than even, and the rolling of 24 is worse.