On a roll of two dice (die), we shall say that Bob wins if atotal of 2,3,4,11,12
ID: 2953234 • Letter: O
Question
On a roll of two dice (die), we shall say that Bob wins if atotal of 2,3,4,11,12 occurs. a) What is the probability Bob wins? b) On 4 rolls of the two die, what is the probability Bob winsexactly once? c) On 4 rolls of the two die, what is the probability that Bobwins two consecutive times? d) On 4 rolls of the two die, what is the probability that Bobdoes not win? On a roll of two dice (die), we shall say that Bob wins if atotal of 2,3,4,11,12 occurs. a) What is the probability Bob wins? b) On 4 rolls of the two die, what is the probability Bob winsexactly once? c) On 4 rolls of the two die, what is the probability that Bobwins two consecutive times? d) On 4 rolls of the two die, what is the probability that Bobdoes not win?Explanation / Answer
Two dices a) Bob wins if the sum is 2,3,4,11 or 12 There are in total 36 possibilities P(X=2) = 1/6*1/6=1/36 because you need twotimes 1: P(X=3) = 1+2 , 1+2, so 2 out of 36 = 1/18 P(X=4) = 2+2, 1+3 and 3+1 gives 4. So4/36=1/9 P(X=11) = 5+6, 6+5 gives 1/18 P(X=2) = 1/6*1/6= 1/36, because you need two times6. The sum of these chances is the chance that Bob wins. This is 11/36 b) Throw 4 times the dice: Chance Bob wins = 11/36 Chance Bobloses = 1-11/36 = 25/36 P(Bob wins 1 times) = 4* 11/36* 25/36*25/36*25/36 = 0.40 = 40% You have to multiply it by 4, because there are 4 possibilties. Bobcan win the first time, second time, third time or the fourth andlast time c) P(Bob wins 2 consecutive times) = Bob wins first and second time orsecond and third time, or third and fourth time) These means that there are 3 possibilities The change of each possibility is: 11/36*11/36*25/36*25/36= 0.045 Now, multiply this by 3, because there are 3 possibilities So, the change that Bob wins 2 consecutive times is 0.135 =13.5% d) P(bob loses everytime) = 25/36*25/36*25/36*25/36= 0.23 =23% I hope you understand this. Your question is a lot of work, becauseit are actually 4 questions. Good Luck further :)