Question

Let k be the total number of heads in two independent tosses of the coin. Find pq|k(3/4|2) .

Answer 1

Suppose we have 3 unbiased coins and we have to find the probability of getting at least 2 heads, so there are 23 = 8 ways to toss these coins, i.e., HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Out of which there are 4 set which contain at least 2 Heads i.e., HHH, HHT, HH, THH So the probability is 4/8 or 0.5So Probability ( getting at least 4 heads )=1/2⁶

Method 1 (Naive)

A Naive approach is to store the value of factorial in dp[] array and call it directly whenever it is required. But the problem of this approach is that we can only able to store it up to certain value, after that it will lead to overflow.

Answer 2

Answer:

Let the random variable X denote the number of heads in three independent tosses of a fair coin. Find the PMF of X. Also find the CDF of X. PMF of X: x p(x).