Question

One ordinary quarter and a fake quarter with two heads are placed in a hat. one quarter is selected at random and tossed twice . If the outcome is "HH" what is the probability that an ordinary quarter was selected?

Answer 1

Help me pleaseee

Answer 2

P(HH) = P(HH | T) + P(HH | F)

P(HH | T) = (1/4) (1/2) = 1/8
P(HH | F) = (1) (1/2) = 1/2
P(HH) = (1/2) + (1/8) = 5/8

P(T | HH) = P( HH & T) / P( HH) = (1/8) / (5/8) = 1/5

Answer 3

okay thank you so the answer is 1/5 i have another question to ask you.

Answer 4

in terms of HH outcomes,
2 heads = {HH, HT, TH, TT; HH}, where the first 4 outcomes are from an ordinary quarter, the last outcome is from the fake quarter
HH outcome from the true coin = 1, number of outcomes in the experiment = 5
P = 1/5