Question

Flipping a fair coin or a weighted coin. Assume that the weighted coin yields a heads with probability 0.4. You select one of the coins at random, and flip it 2 time, noting heads or tails with each flip.
What is the probability that the weighted coin was selected, given that all 2 flips turned up heads____________?

Answer 1

How have you been?

Answer 2

Given the coin is weighted, probability of flipping 2 heads is (.4)^2 = .16 or 4/25
Let W be weighted, F means fair coin and H mean 2 heads
P(H|W) = 4/25
P(H|F) = 1/4
P(H) = (1/2)(4/25) + (1/2)(1/4) = 41/200

P(W|H) = [(1/2)(4/25)]/(41/200) = 16/41

Answer 3

i am assuming there are only 2 coins to choose from...1 weighted and 1 fair
is that right?

Answer 4

Yes

Answer 5

you are correct