Question

6. (15 pts) When a fair dice is thrown, the probability of getting an ace is p= 1/6. a) (4 pts) If a person throws this dice for four times, what is the probability that he will get no more than one ace? b) 6 pts) If he/she throws this dice for 300 times, what is the probability that he will get more than 55 aces? c) pts) If the dice is not fair, the probability of getting an ace for each throw is p=1/50. For 100 throws, what is the probability that he will get at least 4 aces?

Answer 1

The solution to this problem is given by

Solution Let live 'x' denote 'member of success and in the n thail n sample) Preobabelity of succes (or and o denote (9) le pohobability of ace = // n=4 & P( XL) no { P(X=2) "Xu Binomial 21 in=4 where P(X=x) =n cub maha 'cx (2)*(8j4* {iqz1-bg = 0.8680 na Aw 0.8680 ) Now 300,b=1 P (More than 55 aces) = P(x>55) 1-P(X<55) - I Ź 30 DC (4)" ( ) Xu Binonial with n=300,b=7 55 300-2 1 x=0 0.804260 0.1957 1 1 i

(C) pi bo 10 luora 49 Бо n=100 Now XwiBinomial (noloo, lo = 1/2) "P(X=1) = Cali) ( un Plat least 4 aces) fee :P (824) |-P(X24 ) HP(x3) = 1- & Plana = 0.858.96 - 10.1410