Chapter 10.2, Problem 12E

To determine

To calculate:

The probability value of picking number $3$ and number greater than $10$ in the first and second draw

Answer to Problem 12E

The required probability of events is $0.025$

Explanation of Solution

Given information:

Numbers: $1-25$

Calculation:

In the first draw, need to select the number $3$ from $25$ numbers. So, its probability is calculated as:

  $P\left(A\right)=\frac{1}{25}$

In the next draw, need to select the number greater than $10$ from $25$ numbers. It is $11$ to $25$ . So, its probability is calculated as:

  $P\left(A\right)=\frac{15}{24}$

Now, the probability of the independent event is calculated as:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=\frac{1}{25}\times \frac{15}{24}\\ P\left(A\cap B\right)=0.025\end{array}$