Question

What is the probability that the random variable X (which is the number of Heads from flipping a coin 5 times) is equal to 0?

Answer 1

Given that the random variable X is the number of Heads from flipping a coin 5 times. X can take values {0,1,2,3,4,5}. When coin is tossed five times then number of event in sample space i.e. # (Sample Space)=2⁵=32. Only once it happens that no head (all tails) appear after flipping coin. Therefore, the required probability=(1/32). Thus, P(X=0)=1/32=0.03125.

Another way:

Assuming that the trials are independent and the coin is unbiased, i.e. the event of getting a head or a tail in each toss are equally likely which means that P(head) = P(tail) = 0.5,
We can use Binomial distribution as:
The probability mass function of binomial distribution is given by
P(X=x) = (nCx)* p^x* q^(n-x)
where, n = no. of trials;x = no of success;n-x = no of failure;p = probability of success;q = probability of failure and p+q =1
Here n=5, p=q=0.5
Probability of zero heads=P(X=0)=(5C0)* (0.5)^0 *(0.5)^5 =0.03125.