Question

The Sky Ranch is a supplier of aircraft parts. Included in stock are 10 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected without replacement. Let the random variable x represent the number that are not correctly calibrated.

Answer 1

Answer:  a) 0.545,b) 0.41, c) 0.045, d) not possible.

Step-by-step explanation:

The Sky Ranch is a supplier of aircraft parts. Included in stock are 10 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected without replacement. Let the random variable

x represent the number that are not correctly calibrated.

Complete the probability distribution table.

x={0,1,2,3}

P(x=0)=?

P(x=1)=?

P(x=2)=?

P(x=3)=?

Since we have given that

n = 12

number of good one = 3 from 10

number of bad one = 2

So, P(X=0)=$\dfrac{^{10}C_3\times ^2C_0}{^{12}C_3}=\dfrac{120}{220}=0.545$

P(X=1) = $\dfrac{^{10}C_2\times ^2C_1}{^{12}C_3}=\dfrac{90}{220}=0.41$

P(X=2)=$\dfrac{^{10}C_1\times ^2C_2}{^{12}C_3}=\dfrac{10}{220}=0.045$

P(X=3) is not possible.

Hence, a) 0.545,b) 0.41, c) 0.045, d) not possible.