Question

. A hat contains 100 coins, where 99 are fair but one is double-headed (always landing Heads). A coin is chosen uniformly at random. The chosen coin is flipped 7 times, and it lands Heads all 7 times. Given this information, what is the probability that the chosen coin is double-headed?

Answer 1

Answer:0.565

Step-by-step explanation:

Hat contain 100 coins out of which 99 is fair and one is double headed.

Probability of getting 7 heads is sum of Head through fair coin+heads through biased coin

Probability of getting a head through a fair coin=0.5

$P(7 heads)=0.99\times 0.5^7+0.01\times 1$

$P(Double head |7 heads )=\frac{Probability\ of\ 7\ heads\ and\ double\ headed}{probability\ of\ 7\ heads}$

$P(Double head |7 heads )=\frac{0.01\times 1}{0.99\times 0.5^7+0.01\times 1}$

$=\frac{0.01}{0.99\times 0.0078+0.01}=0.565$