Question: A fair coin is ipped 3 times. The toss results are recorded on separat

Question

Question: A fair coin is ipped 3 times. The toss results are recorded on separate slips of paper (writin... A fair coin is ipped 3 times. The toss results are recorded on separate slips of paper (writing “H” if Heads and “T” if Tails), and the 3 slips of paper are thrown into a hat. (a) Find the probability that all 3 tosses landed Heads, given that at least 2 were Heads. (b) Two of the slips of paper are randomly drawn from the hat, and both show the letter H. Given this information, what is the probability that all 3 tosses landed Heads?

Explanation / Answer

(a) There are three ways in which 2 outcomes are heads and one is tails.

There is one way in which all 3 outcomes are heads.

=> Probability that all three are heads given that atleast 2 are heads = 1 / (1 + 3) = 1/4 = 0.25.

(b) The probability of getting heads on third toss = 0.5.

=> Probability that all 3 tosses landed heads given that two landed heads = 0.5.

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