Question

I flip three fair coins, each with a 50-50 probability of getting heads or tails. I do not show you the results, but I tell you that at least one of the three coins shows heads. Given this information, calculate the conditional probability that exactly two of the three coins show heads.

Answer 1

Answer:3/7

Explanation:

Since a coin has a head(H) and a tail(T), if two coins are flipped, the total outcome will be 4 i.e(HH, HT, TH and TT)

If 3coins are now flipped, then we will have 8total possible outcomes. The general formula being '2^n' where n is the number of coins.

The outcomes will be matching (H,T) with (HH, HT, TH, TT) to give (HHH, HHT, HTH, HTT, THH, THT, TTH and TTT). Since at least one if the 3coins shows head, then we have 7total possible outcomes excluding TTT.

Probability that exactly two of the three coins shows head (possible outcome/total outcome)

Exactly 2heads are HHT,HTH and THH(3possible outcomes)

Total outcome is 7

P(exactly two heads) = 3/7