Question

At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 74% of landing tails. What is the probability of choosing the biased coin if you won a prize. a. 0.2600 b. 0.5968 c. 0.3421 d. 0.5243 e. None of the above

Answer 1

c. 0.3421

Explanation:

The computation of the probability of selecting the biased coin is shown below:

The probability of any coin selected is 1 ÷ 2

The probability in the case when the biased coin chosen & wins 1 ÷ 2 (1 - 0.74)

And, the win probability is 1 ÷ 2 (1 - 0.74) + 1 ÷ 2 (1 - 0.5)

Now the probability of biased or win is

= {1 ÷ 2 (1 - 0.74)} ÷ { 1 ÷ 2 (1 - 0.74) + 1 ÷ 2 (1 - 0.5)}

= 0.13 ÷ 0.38

= 0.3421

Hence, the correct option is c. 0.3421