A coin is tossed 5 times Find the probability that exactly 3

A coin is tossed 5 times. Find the probability that exactly 3 are tails. Find the probability that at most 2 are tails. The probability that exactly 3 are tails is (Type an integer or decimal rounded to the nearest thousandth as needed.) The probability that at most 2 are tails is (Type an integer or decimal rounded to the nearest thousandth as needed.)

Solution

As per Bernouli’s formula, the probabilty of exactly x events happening out of n times is

nC_x * p^x * (1-p)^1-x

Here, n= 5 x= 3. Then, the probabilty that exactly 3 are tails

5C3 * (1/2)³ * (1/2)²

= 5C3 * (1/2)⁵

= 10* 1/32

= 5/16 = 0.313

P (at most 2 tails) = P(0,or 1, or 2 tails) = (1/32) + (5/32) + 5C2(1/2)⁵ = 6/32 + 10/32 = 16/32 = 1/2 = 0.5