Question

You have a bag with 100 pennies. One of the 100 pennies is weighted so that it lands on heads 90% of the time. The rest of them land on heads 50% of the time. You pull out a random coin and ip it ve times in a row. It lands on heads every single time. What is the probability that it is the weighted penny?

Answer 1

Answer:

0.160275

Step-by-step explanation:

P(5 time heads) =P(fair penny and 5 time heads + weighted penny and  5 time heads)

probability of fair penny = 99/100 (as one is removed)

probability of heads = 50% = 0.5 flipped 5 times

probability of weighted penny = 1/100

probability of heads for this penny = 90% = 0.9

substituting, we have

=(99/100) * (1/2)*5  +  (1/100) * (0.9)5  = 0.036842

hence from Bayes theorem

P(weighted penny | 5 time heads) =P(weighted penny and 5 time heads) / P(5 time heads)

=(1/100)*(0.9)5 /0.036842 =0.160275