Question

76. A company has hired 10 new employees, I men and 3 women. The company mustassign 5 of them to the morning shift, 3 of them to the swing shift, and the restof them to the graveyard shift.(a) (2 points) Find the prob that at least one man is assigned to the swing shift?

Answer 1

`(2519)/(2520)`

Step-by-step explanation:

Here, we want to get the probability that at least one man is assigned to the swing shift

From the question, 3 of the employees are assigned to the swing shift

Thus we have to calculate the probability of:

1 man , 2 men or 3 men

Mathematically, we have that as:

1 - p(all of the swing shift employees are women)

For the swing shift, for all them to be women, we will be selecting 3 out of 3 so the combination here is 3 C 3 which is 1

We now calculate the probability by dividing this value by the total number of possible ways

Mathematically, we have that as follows:

`\frac{1}{10\text{ C 5 }*\text{ 5 C 3 }^*\text{ 1}}\text{ = }(1)/(2520)`

This is the probability of placing all of the women on the swing shift

So, the probability that at least 1 man is assigned will be:

`1-\text{ }(1)/(2520)\text{ = }(2519)/(2520)`