Question

A. Directions: Tossing four coins. Suppose four coins are tossed. Let Y be

the random variable representing the number of tails that occur. Complete

the table below by showing the values of random variable Y.

Let H = Heads

T = Tails

Answer 1

The possible number of tails (Y) is: 0,1,2,3,4.

Computing the respective probabilities using the binomial distribution and assuming that the probability of a tail and the probability of a head are equal:

1. $P(Y=0)=\left(\frac{1}{2}\right)^4=\frac{1}{16}$
2. $P(Y=1)=C_4^1\left(\frac{1}{2}\right)^4=4\left(\frac{1}{2}\right)^4=\frac{1}{4}$
3. $P(Y=2)=C_4^2\left(\frac{1}{2}\right)^4=\frac{3\cdot4}{2}\left(\frac{1}{2}\right)^4=\frac{3}{8}$
4. $P(Y=3)=C_4^3\left(\frac{1}{2}\right)^4=\frac{1}{4}$
5. $P(Y=4)=C_4^4\left(\frac{1}{2}\right)^4=\frac{1}{16}$

The Probability distribution of Y

$\begin{matrix}Y&{0}&{1}&{2}&{3}&{4}\\p&{\frac{1}{{16}}}&{\frac{1}{{4}}}&{\frac{3}{{8}}}&{\frac{1}{{4}}}&{\frac{1}{{16}}}\end{matrix} ​$