Question

Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution.

- Let$\mathrm{x}=$the number of years a student will study ballet with the teacher.

- Let$\mathrm{P}\left(\mathrm{x}\right)=$the probability that a student will study ballet$\mathrm{x}$years

Short answer

Probability of$\mathrm{P}(\mathrm{x}<4)$is $0.25$.

Step-by-step solution

Given information

$\mathrm{x}$is the number of years a student will study ballet with the teacher.

$\mathrm{P}\left(1\right)=0.10$.

$\mathrm{P}\left(2\right)=0.05$.

$\mathrm{P}\left(3\right)=0.10$

Calculation for probabiltiy

Table as,

From table,

$\mathrm{P}(\mathrm{x}<4)=\sum _{\mathrm{i}=1}^3\mathrm{P}\left({\mathrm{x}}_{\mathrm{i}}\right)$

$=0.10+0.05+0.10$

$=0.25$