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Question
A fair coin is tossed 12 times. Find the probability of getting exactly 7 heads .
Solution
Let X denote number of heads obtained in 12 tosses.
∴ X = 0, l , 2, 3, 4, 5 , 6, 7, 8, 9, 10, 11, 12
n = 12
p : Probability of getting head in a single toss.
∴ p = `1/2`
q = `1 - 1/2 = 1/2`
The binomial distribution is
x ~ B `(12 , 1/2)`
∴ p.m.f. is P(X = X) = `"^n C _x p^x q^(n-x)`
P(X = 7) = `"^12 C _7 (1/2)^7 (1/2)^5`
`= "^12 C _7 (1/2)^12`
`= 792 xx (1/2)^12`
`= 792 xx 1/4096`
= 0.193
∴ Probability of getting exactly 7 heads is 0.193
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