Chapter 2 Section 2 Question 1

Question

Consider flipping two independent fair coins. Let X be the number of heads that appear. Compute $P(X=x)$ for all real numbers x.

Answer

Author: Mohammad-Ali Bandzar| Date:Oct 14 2020

The possible outcomes from flipping two coins are as follows:

Heads,Heads

Heads,Tails

Tails,Heads

Tails,Tails

The probability of no heads is $\frac{1}{4}$ therefore $P(X=0)=\frac{1}{4}$

The probability of one head is $\frac{1}{2}$ therefore $P(X=1)=\frac{1}{2}$

The probability of two heads is $\frac{1}{4}$ therefore $P(X=2)=\frac{1}{4}$

the probability of any other number of heads is zero $P(X=x)=0$ for $x\notin \{0,1,2\}$

The possible outcomes from flipping two coins are as follows:

Heads,Heads

Heads,Tails

Tails,Heads

Tails,Tails

The probability of no heads is $\frac{1}{4}$ therefore $P(X=0)=\frac{1}{4}$

The probability of one head is $\frac{1}{2}$ therefore $P(X=1)=\frac{1}{2}$

The probability of two heads is $\frac{1}{4}$ therefore $P(X=2)=\frac{1}{4}$

the probability of any other number of heads is zero $P(X=x)=0$ for $x\notin \{0,1,2\}$