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?

Question

Danielle

Mathematics

23 August, 11:23

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?

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Answers (1)

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Big Mac · Answer 1

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