Chapter 13.6, Problem 10CFU

To determine

The solution of the probability.

Answer to Problem 10CFU

  $0.96922$ .

Explanation of Solution

Given information:

Jasmine Myers, a weather reporter for channel $6$ ,is forecasting a $30\%$ chance of rain for today and the next four days. Find each probability.

  $P($ Having no more than three days $)$

Calculation:

From the given information, weather reporter for channel $6$ ,is forecasting a $30\%$ chance of rain for today and the next four days.

  $P($ Having rain no more than three days $)$

  $=1-P($ rain more than three days $)$

  $=1-([P(\text{rain on 4 days)+}P(\text{rain on }5\text{ days}))$

Now, conclude that:

  $P($ Having rain no more than three days $)$

  $=1-(C(5,4)\cdot {0.3}^4\cdot {0.7}^1+C(5,5)\cdot {0.3}^5\cdot {0.7}^0)$

  $\begin{array}{l}=1-(0.02835+0.00243)\\ =0.96922\end{array}$

Thus, the solution of the probability is $0.96922$ .