The unemployment rate in a city is 13%. If 6 people from the city are sampled at random, find the probability that at least 3 of them are unemployed. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

The probability that at least 3 of them are unemployed is 0.97 if the unemployment rate in a city is 13%. If 6 people from the city are sampled at random.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The unemployment rate in a city is 13%. If 6 people from the city are sampled at random, find the probability that at least 3 of them are unemployed.

Let's suppose:

X(i) = {1 ; if person is unemployed}

0; otherwise

P[x(i) = 1] = 0.13

P[x(i) = 0] = 1 - p = 0.87

X = ∑(i =1 to 6) = Number of people unemployed

Here x binomial [n - 6, p = 0.13]

P[X = x] = C(6, x)(0.13)ˣ(0.87)ˣ, x = 0,1,2,3...6

The probability:

P[X<3] = P(X = 0) + P(X = 1) + P(X = 2)

= C(6, 0)(0.13)°(0.87)° + C(6, 1)(0.13)(0.87) + C(6, 2)(0.13)²(0.87)²

= 0.97

Thus, the probability that at least 3 of them are unemployed is 0.97 if the unemployment rate in a city is 13%. If 6 people from the city are sampled at random.

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