SOLUTION: Question #9: Working Women and Computer Use It is reported that 72% of working women use computers at work. Choose 5 working women at random. Find a. The probability that at le

Question 1194572: Question #9: Working Women and Computer Use
It is reported that 72% of working women use computers at work. Choose 5 working women at random. Find
a. The probability that at least 1 doesn’t use a computer at work

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

This is a binomial probability distribution problem.

n = 5 = sample size
p = 1-0.72 = 0.28 = probability of a woman not using a computer at work.

The binomial probability formula we'll use is this
P(x) = (n C x)*(p)^x*(1-p)^(n-x)
The n C x refers to the nCr combination formula.
x = number of women who do not use a computer at work

Plug in x = 0 to find the probability of exactly 0 women not using a computer at work
P(x) = (n C x)*(p)^x*(1-p)^(n-x)
P(0) = (5 C 0)*(0.28)^0*(1-0.28)^(5-0)
P(0) = (1)*(0.28)^0*(1-0.28)^(5-0)
P(0) = 0.1934917632

Then compute the complementary probability.
P(at least one does not use a computer) = 1 - P(zero women do not use a computer)
P(at least one does not use a computer) = 1 - P(0)
P(at least one does not use a computer) = 1 - 0.1934917632
P(at least one does not use a computer) = 0.8065082368
This works because we have two options: Either zero women do not use a computer at work, or at least one woman does not use a computer at work.

The longer method would be to compute it like this
P(X ≥ 1) = P(1) + P(2) + P(3) + P(4) + P(5)
I'll let you compute the individual values P(1) through P(5). Follow similar steps mentioned when I computed P(0).

Answer: 0.8065082368
Round this value however your teacher instructs.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Question #9: Working Women and Computer Use
It is reported that 72% of working women use computers at work.
Choose 5 working women at random. Find
a. The probability that at least 1 doesn’t use a computer at work
~~~~~~~~~~~~~~~~~~

The probability that one randomly selected working women uses a computer at work is 0.72, according to the problem. The probability that of 5 randomly selected working women all 5 use computers at work is = 0.193492 (rounded). The probability that of 5 randomply selected working women at least one doesn't use a computer at work is the complement to it P = 1 - = 1 - 0.193492 = 0.806508 = 80.6508%. ANSWER

Solved.

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To see many other similar (and different) solved problems of this type, look into the lessons
    - Solving probability problems using complementary probability
    - Solving probability problems using complementary probability REVISITED
in this site.

Learn the subject from there.

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