Question

Consider the experiment of tossing a coin three times (Prob. 1.1). Let X be the random variable giving the number of heads obtained. Assume that the tosses are independent and the probability of a head is p. (a) What is the range of X? (b) Find the probabilities P(X = 0), P(X = I), P(X = 2), and P(X = 3).

Answer 1

A coin tossed three times. Total number of outcomes are $8.$

Let $S$ be sample space.

Then $S=$ {$HHH,HHT,HTH,HTT,THH,THT,TTH,TTT$ }

Let $X$ be a random variable giving number of heads obtained.

Then $X$ can take the values $0,1,2,3.$

(a) The range of $X$ is $=$ {$0,1,2,3$ }

(b) $P(X=0)=$ probability of getting no head $=\frac{1}{8}$

$P(X=1)=$ probability of getting one head $=\frac{3}{8}$

$P(X=2)=$ probability of getting two heads $=\frac{3}{8}$

$P(X=3)=$ probability of getting three heads $=\frac{1}{8}$