Question

The probability that an individual is left-handed is 12%, In a randomly selected class of 30students, what is the probability of finding exactly 4 left-handed students?

Answer 1

Given that:

- The probability that an individual is left-handed is 12%.

- There are 30 students in the class.

You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :

`P(x)=(n!)/((n-x)!x!)p^x(1-p)^(n-x)`

Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.

In this case:

`\begin{gathered} n=30 \\ x=4 \\ p=(12)/(100)=0.12 \end{gathered}`

Therefore, by substituting values into the formula and evaluating, you get:

`P(x=4)=(30!)/((30-4)!4!)(0.12)^4(1-0.12)^(30-4)`
`P(x=4)\approx0.2047`

Hence, the answer is:

`P(x=4)\approx0.2047`