Question

Assume that when adults with smartphones are randomly​ selected, 61% use them in meetings or classes. If 8 adult smartphone users are randomly​ selected, find the probability that exactly 3 of them use their smartphones in meetings or classes

Answer 1

0.1147

Explanation:

When adults with smartphones are randomly​ selected, 61% use them in meetings or classes, then

• the probability of using the smartphone is
  `p=0.61;`

• the probability of not using the smartphone is
  `q=1-p=1-0.61=0.39.`

If 8 adult smartphone users are randomly​ selected, the probability that exactly 3 of them use their smartphones in meetings or classes can be calculated using binomial distribution as

`C^8_3\cdot p^3\cdot q^(8-3)=C^8_3\cdot (0.61)^3\cdot (0.39)^5`

Note that

`C^8_3=(8!)/(3!(8-3)!)=(5!\cdot 6\cdot 7\cdot 8)/(2\cdot 3\cdot 5!)=(6\cdot 7\cdot 8)/(2\cdot 3)=7\cdot 8=56,`

then the probabilty is

`56\cdot (0.61)^3\cdot (0.39)^5\approx 0.1147`