One coin in a collection of 65 coins has two heads; the rest of the coins are fair. If a coin, chosen at random from the lot and then tossed, turns up heads six times in a row, what is the probability that it is the two-headed coin?

Question

Sebastian Boyd

Mathematics

11 September, 18:56

One coin in a collection of 65 coins has two heads; the rest of the coins are fair. If a coin, chosen at random from the lot and then tossed, turns up heads six times in a row, what is the probability that it is the two-headed coin?

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Slade · Answer 1

There is only 1 two-headed coin in the collection of 65 coins.

The probability of selecting the two headed coin is 1/65.

The outcome achieved when any of the other coins is tossed a number of times is based purely on chance.

Although if the 2-headed coin is selected, the only possible outcome is having a head, but It also possible to have 6 heads in 6 tosses with a coin that is not 2-headed.

What we're concerned with, is the probability that the 2-headed coin was selected from the lot of 65 coins, which is 1/65.