Question

In tossing 5 coins what's the probability of obtaining fewer than 3 heads?

Answer 1

Every coin has two outcomes, one is the head and the other is the tail. Letus we call head as a success.

Therefore, the probability of success = probability of head = p = 0.5 ----------------------(if the coin is fair)

Now, let X = Number of heads in the experiment of tossing 5 coins = number of success in 5 trials

Here, X follows Binomial distribution with parameter n=5 and probability of success, p=0.5.

Therefore, pmf of x is,

Now, the probability of obtaining fewer than 3 heads = Probability of successes fewer than 3

= P(X<3)

= P(X=0) + P(X=1) + P(X=2)

= 0.03125 +0.15625 + 0.3125 =0.5

Therefore, ?the probability of obtaining fewer than 3 heads is 0.5.