Question 613620: Timmy has two irregular coins. The nickel comes up heads three fifths of the time, and the quarter comes up heads two thirds of the time. The nickel is tossed.
If the nickel comes up heads, then the quarter is tossed twice.
If the nickel comes up tails, the quarter is tossed once. Find the probability that exactly two tails come up.
[Nickel is 3/5 = .6; Qtr is 2/3 = .67; .6 + .67 = 1/27 and .6 * .67 = .402
.67 - .402 = .268
If I read this correctly, we are looking for the probability of the nickel coming up tails 2x. So (?) to find the correct answer do I:
1-.6 * .268 to equal .839. Now THAT is not the correct answer! LOL! Your detailed explination how to find the correct answer is greatly appreciated!]
Thaning you in advance, Diane
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! following the tossing instructions, there are six possible outcomes
___ hHH, hHT, hTH, hTT, tH, tT
there are two ways to get 2 tails ___ hTT or tT
like the basketball problem, the probability of any string is the product of the individual probabilities
hTT __ 3/5 * 1/3 * 1/3 = 1/15
tT ___ 2/5 * 1/3 = 2/15
these are two of the possible strings, so their probabilities add to give the probability for the 2 tail combination
probability of two tails ___ 1/15 + 2/15 = 3/15 = 1/5 = .2
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