Chapter 10.1, Problem 26E

To determine

To find: the probability that the given graph intersects the x-axis.

Answer to Problem 26E

The probability that the given graph intersects the x-axis is 0.33.

Explanation of Solution

Given:

  

Calculation:

From the given graph, $y=f\left(x\right)+c$ intersects the x axis when c is a randomly chosen integer from 1 to 6.

When all outcomes are equally likely, the theoretical probability is described as the ratio of number of favourable outcomes to total number of outcomes.

There are 6 outcomes, and the graph intersects the x axis at point 2. Therefore, the probability that the graph of $y=f\left(x\right)+c$ intersects the x axis when c is a randomly chosen integer from 1 to 6 is as follows:

  $\begin{array}{l}P\left(A\right)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\\ =\frac{2}{6}\\ =0.33\end{array}$

Conclusion:

The probability that the given graph intersects the x-axis is 0.33.