Chapter 0, Problem 21PR

To determine

To calculate: Probability the coin land on head and the number rolled in greater than 4.

Answer to Problem 21PR

Theprobability of the coin lands on head and the number rolled in greater than 4 is $\frac{1}{6}.$

Explanation of Solution

Given information:

Possible outcome in coins = H or T

Possible outcome in dice = 1,2,3,4,5 or 6

Calculation:

Here, possible outcome when the dice is rolled and coin is tossed is-

  $S=\{\left(1,H\right),\left(2,H\right),\left(3,H\right),\left(4,H\right),\left(5,H\right),\left(6,H\right),$ and

  $\{(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}$

Lets, E be the event the coin lands on head and the number rolled is greater than 4.

Therefore,

  $\begin{array}{l}E=\{\left(5,H\right),\left(6,H\right)\}\\ \therefore P(E)=\frac{n(E)}{n(S)}\\ P(E)=\frac{2}{12}=\frac{1}{6}\end{array}$

So, theprobability of the coin lands on head and the number rolled in greater than 4 is $\frac{1}{6}.$