# Find at Least Three Heads?

Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads?

- 99
- 102
- 103
- 104

**Answer: (1) 99**

**Explanation:-
**Let the number of heads obtained in a throw of 7 coins = X

Then, X = B(n = 7, p = 12)

The probability mass function is p(x) = 7Cx (12)x (12)7 – x x = 0, 1, 2,…….,7

P(at least 3 heads) = 1 – P(at most 2 heads)

= 1- {p(0) + p(1) + p(2)}

= 1- {7C0 (1/2)7 + 7C1 (1/2)7 + 7C2(1/2)7 } = 99/128

The number of tosses resulting in at least 3 heads = n XP(at least 3 heads)

= 128 × 99/128 = 99

Then, in 99 tosses we expect at least 3 heads to occur.

Hence, the answer is (1) 99.