Please Help! 22 A gambler has one pair of fair dice and one pair of loaded (unfair) dice. For the loaded dice,the probability of rolling a sum of seven is 1/5. If a pair of dice is chosen at random and asum of seven occurs, what is the probability the dice were loaded?а) 613g) none of the othersc) 35d) 1/6e) 6/11 f 1/36b) 12

Name: Please Help! 22 A gambler has one pair of fair dice and one pair of lo
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please Help! 22 A gambler has one pair of fair dice and one pair of loaded (unfair) dice. For the loaded dice,the probability of rolling a sum of seven is 1/5. If a pair of dice is chosen at random and asum of seven occurs, what is the probability th

Consider the following events, A=chosen pair of dice is fairB=chosen pair of dice is loadedE=sum of 7 is obtained Since choosing a pair of dice from the two, is equally likely, PA=PB=12 Also, for a fair dice, total possible outcomes are 36, but only 6 of them 1,6,2,5,3,4,4,3,5,2,6,1 will yield a sum of 7, so the probability is given by, PEA=636=16 From the given data, PEB=15As per the Bayes' theorem, PBE=PB·PEBPB·PEB+PA·PEA Substitute the values, PBE=12·1512·15+12·16=110110+112=11+1012=1212+10=611Thus, the probability that the sum was obtained from the loaded dice, is equal to 611. Therefore, option (e) is the correct choice.