4. (On Rolling Dice and Application of Complementation Rule) (a) Suppose you rol

Question

4. (On Rolling Dice and Application of Complementation Rule) (a) Suppose you roll a fair die four times. What is the probability that you will get at least one "6"? (b) If you roll two fair dice simultaneously, what is the probability that you will get a double-six, that is, a "(6,6)"? get at least one double-six in these 24 rolls? expect this result (c) Now, suppose you roll two fair dice simultaneously 24 times, what is the probability that you will (d) Compare the probability in (a) and (c). Which has a higher probability? Did you (intuitively)

Explanation / Answer

a) probability of a six on one roll =1/6

probability of getting at least one 6 in 4 rolls =1-P(no six in 4 rolls) =1-(1-1/6)4 =1-625/1296 =671/1296=0.5177

b)probability of double six =1/36 (as it is one event out of total 36 events whcih occur on rolling of two dice,

c)probability of getting double six ; at least once in 24 rolls =1-P(getting none double six)

=1-(1-1/36)24 =0.4914

d) probability in part a is higher.

we expect this result as propability of a six is higher and numebr of outcome in expermient in a is less than in part c)

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