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If the probability of hitting a target when throwing a dart is five out of seven and if six darts are thrown what is the probability of getting exactly four hits?
Tcote
Compute the probability of any specific sequence of hits and misses, such as HMHHHM, by multiplying the probabilities of each throw: 5/7 for each hit ("H") and 1 - 5/7 = 2/7 for each miss ("M"). Because there are four hits (and therefore two misses), the multiplication includes four factors of 5/7 and two factors of 2/7; briefly, the product equals 5^4 * 2^2 / 7^6. There are 15 distinct sequences of four hits and two misses. Therefore the probability of getting some sequence of exactly four hits equals 15 times this previous value: 15 * 5^4 * 2^2 / 7^6 = 37500 / 117649 = about 31.87%.
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