SOLUTION: Two coins are available, one is fair and other is two headed. Choose a coin and toss it once; assume that unbiased coin is chosen with probability 3/4 give that the outcome is head

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Question 1184301: Two coins are available, one is fair and other is two headed. Choose a coin and toss it once; assume that unbiased coin is chosen with probability 3/4 give that the outcome is head. The probability that the two headed coin was chosen is:
A- 3/5
B- 2/5
C- 1/5
D- 2/7
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Correct option is:2%2F5

Let F+denotes fair coin.
T+denotes two headed,
H denotes head occurs
P%28F%29=+3%2F4
P%28T%29=1-3%2F4=+1%2F4

.......(By Baye's theorem)
= %281%2A%281%2F4%29%29%2F%281%2A%281%2F4%29%2B%281%2F2+%29%2A%283%2F4+%29%29
= %281%2F4%29%2F%281%2F4%2B3%2F8+%29
= %281%2F4%29%2F%285%2F8+%29
= 8%2F%284%2A5+%29
=+2%2F5+


Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.

The @MathLover1 solution is copied from     (or inspired by)
https://www.toppr.com/ask/en-us/question/two-coins-are-available-one-fair-and-the-other-twoheaded/


without making a reference.