A bag has 4 fair coins (1 head 1 tail) and 4 double-headed coins. A coin is drawn and flipped 3 times all heads. Probability it's double-headed?
Show answer & explanation
Correct answer: B
Explanation
4 Fair Coins, 4 Two-headed Coins
One coin is selected.
Upon being tossed 3 times, it landed heads every time.
P(Two-headed) = 4/8 = 1/2
P(Fair) = 1/2
P(3 Heads | Two-headed) = 1
P(3 Heads | Fair) = (1/2)³ = 1/8
P(Two-headed | 3 Heads)
= [(1/2)×1] / [(1/2)×1 + (1/2)×(1/8)]
= (1/2) / (1/2 + 1/16)
= (1/2) / (9/16)
= 8/9