Question

A fair coin is tossed 12 times. Find the probability of getting exactly 7 heads .

Answer 1

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