Question

A box contains 4 coins: coin1 has both sides tails; coin2 has both sides heads; coin3 has both sides heads; coin4 is a regular coin (one side heads, one side tails)

a) If we randomly choose one coin from the box and flip, what is the probability we get heads?

b) Suppose we randomly choose a coin, flip, and get heads. What is the probability that the coin that was chosen is the regular coin?

Answer 1

(a)

P(Choosing Coin 1) = P(choosing Coin 2) = P(Choosing coin 3) = P(Choosing coin 4) = 0.25

P(Head from coin1) = 0

P(Head from coin2) = 1

P(Head from coin 3) = 1

P(Head from coin 4) = 0.5

Thus, P(Chhosing one coin & Getting Head) = (0.25 X 0) + (0.25 X 1) + (0.25 X 1) + (0.25 X 0.5) = 0.625

(b)

Let

A = getting head

Let B1, B2, B3 , B4 be the events of choosing coin 1, coin 2, coin3 and coin 4 respectively.

P(A/B1) = 0

P(A/B2) = 1

P(A/B3) = 1

P(A/B4) = 0.5

By Baye's Theorem:

= 0.125/0.625 = 0.2