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If 10 coins are tossed, you could get 4 heads and 6 tails, 3 heads and 7 tails, 2 heads and 1 tail, 0 heads and 10 tails all giving fewer heads than tails.

Using the binomial distribution ,

P(4 heads) = 10C4 (.5)^4 (.5)^6 = 0.205078.

P(3 heads) = 10C3 (.5)^3 (.5)^7 = 0.117188

P(2 heads) = 10C2 (.5)^2 (.5)^8 = 0.043945

P(1 heads) = 10C1 (.5)^1 (.5)^9 = 0.009766

P(0 heads) =(.5)^10 = 0.000977

Adding all of these probabilities, we have P(fewer heads than tails)= 0.376953

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Related Questions

What is the probability that the first two flips will both be heads and the third flip will be tails if you flip three fair coins?

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