SOLUTION: If Anna flips 8 coins, what is the probability that she gets more heads than tails?

Question 1189397: If Anna flips 8 coins, what is the probability that she gets more heads than tails?

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Technically, the problem needs to state that the coins are fair coins. Assuming that is the case....

The probability of equal numbers of heads and tails (4 each) is

So the probability of NOT getting 4 of each is 186/256.

Then, since the probability of getting more heads than tails is the same as the probability of getting more tails than heads, the probability of getting more heads than tails is 93/256.

ANSWER: 93/256

Of course, you can also answer the problem by finding the probabilities of getting 5, or 6, or 7, or 8 heads:

Finally, you can answer a problem like this quickly if you know how to write out the 8th row of Pascal's Triangle:

1 8 28 56 70 56 28 8 1

Those numbers are C(8,8), C(8,7), ..., C(8,1), and C(8,0). The sum of all those numbers is 2^8=256. So the number of ways of getting more heads than tails is 1+8+28+56=93; and the probability of getting more heads than tails is 93/256.

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