Question

Assume that when adults with smartphones are randomly​ selected, 52​% use them in meetings or classes. If 14 adult smartphone users are randomly​ selected, find the probability that fewer than 4 of them use their smartphones in meetings or classes.

Answer 1

The probability that fewer than 4 of then use their smart phones in meetings  or classes is 0.00030243747.

Step-by-step explanation:

Fewer than 4 means ,less than 4 which is any number less than 4 and not including 4. This is 3, 2,1 and 0. So you find the probability that exactly 3 of then use their smart phone, exactly 2 of them use their smart phones, exactly 1 of them use his/her smart phone and none of them.

Given that 52% use smartphones in meetings and classes =0.52

Thus the remaining 48% do not use smartphones in meetings and classes=0.48

For C(14,3) you will have "14 chose 3", number of ways of choosing 3 out of 14'

=(0.52)³ *(0.48)⁹=0.00019018714

For C(14,2) you will have "14 chose 2", number of ways of choosing 2 out of 14

=(0.52)²*(0.48)¹²=0.00004044841

For C(14,1) you will have "14 chose 1", number of ways of choosing 1 out of 14

=(0.52)¹*(0.48)¹³=0.000037337

For  C(14,0) you will have "14 chose 0", number of ways of choosing 0 out of 14

=(0.52)⁰*(0.48)¹⁴=1*0.00003446492=0.00003446492

The probability that fewer than 4 of them use their smartphones in meetings or classes will be

0.00019018714 +0.00004044841+0.000037337+ 0.00003446492=0.00030243747

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Keywords : Probability, random variable, binomial distribution

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