91影视

The graph for a uniform distribution is given with an area enclosed equally to 1.

There is a one-to-one association between probability and the area of the curve between the range. It holds under the condition when the total area is equal to 1.

Thus,the probability that the waiting time between 2 minutes and 3 minutes would be the same as the area of the shaded region shown below.

Moreover, the area of the shaded region is the difference between the area to the left of 2 minutes and the area to the left of 3 minutes.

The probability that the waiting time is between 2 minutes and 3 minutes is shown below:

$P\left(2<X<3\right)=\text{Area}\text{to}\text{the}\text{left}\text{of}3-\text{Area}\text{to}\text{the}\text{left}\text{of}2...\left(1\right)$

$$\begin{gathered} \text{Area}\text{to}\text{the}\text{left}\text{of}3=\text{Length}脳鈥�\text{width} \\ =0.2脳\left(3-0\right) \\ =0.6...\left(2\right) \end{gathered}$$

$$\begin{gathered} \text{Area}\text{to}\text{the}\text{left}\text{of}2=\text{Length}脳鈥�\text{width} \\ =0.2脳\left(2-0\right) \\ =0.4...\left(3\right) \end{gathered}$$

Substitute (2) and (3) into equation (1).

$$\begin{gathered} P\left(2<X<3\right)=0.6-0.4 \\ =0.2 \end{gathered}$$

Thus, the probability of selecting a passenger randomly when the waiting time is between 2 minutes and 3 minutes is 0.2.