Chapter 13, Problem 43SGA

To determine

To find:The required probability.

Answer to Problem 43SGA

The required probability is $\frac{2}{15}$ .

Explanation of Solution

Given:

Two numbers cubes are tossed.

Calculation:

The probability is given as,

  $P\left(E\right)=\frac{s}{n}$

Here, s is the favorable events and n is the total number of outcomes.

Calculate the probability for getting different match numbers.

  $P\left(A\right)=\frac{6}{36}$

Calculate the probability for getting sum greater than or equal to 5.

  $P\left(B\right)=\frac{30}{36}$

Calculate the probability of A and B.

  $P\left(A\text{ and }B\right)=\frac{4}{36}$

The required probability is calculated as,

  $\begin{array}{c}P\left(A|B\right)=\frac{P\left(A\text{ and }B\right)}{P\left(B\right)}\\ =\frac{\frac{4}{36}}{\frac{30}{36}}\\ =\frac{2}{15}\end{array}$

Thus, the required probability is $\frac{2}{15}$ .