Question

Three coins are tossed. Let T be the number of tails that occur.

a. Construct the probability distribution for the random variable T.

b. Construct the probability histogram

Answer 1

а. We will assume that the probability of getting heads and tails is the same:

$p = q = \frac{1}{2}$

Using Bernoulli's formula, we find the probabilities that 0, 1, 2, and 3 tails will appear:

$p(0) = {q^3} = {\left( {\frac{1}{2}} \right)^3} = \frac{1}{8}$

$p(1) = C_3^1p{q^2} = 3 \cdot {\left( {\frac{1}{2}} \right)^3} = \frac{3}{8}$

$p(2) = C_3^2{p^2}q = 3 \cdot {\left( {\frac{1}{2}} \right)^3} = \frac{3}{8}$

$p(3) = {p^3} = {\left( {\frac{1}{2}} \right)^3} = \frac{1}{8}$

We get the probability distribution:

$\begin{matrix} T&0&1&2&3\\ p&{\frac{1}{8}}&{\frac{3}{8}}&{\frac{3}{8}}&{\frac{1}{8}} \end{matrix}$

b. Construct the probability histogram: