Question

You are going to make 5 assemblies, where each assembly requires the use of 1 Type A Bolt. You have a container of bolts that consists of 20 Type A bolts, 20 Type B bolts, and 20 Type C bolts. At random, you take 10 bolts out of the container. Determine: A) The probability you took the exact number of Type A bolts you need for your 5 assemblies. B) The probability you did not take enough Type A bolts that you need for your 5 assemblies. C) The probability you took more Type A bolts than you need for your 5 assemblies.

Answer 1

Explanation:

You are to make 5 assemblies.

Each assembly requires the use of 1 Type A bolt.

To make the 5 assemblies, you need 5 Type A bolts.

The container of bolts has a total of 60 bolts.

The focus - Type A bolts - is 20 out of this 60.

The probability of obtaining a Type A bolt at all, is 20/60, which is = 1/3

(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?

- The exact number of Type A bolts you need for the 5 assemblies is 5

1/3 × 5/10 = 5/30 = 1/6 = 0.167

(B) What is the probability of taking/having less than 5 Type A bolts out of the randomly selected 10 bolts? The solution is to sum up the following:

1/3 × 4/10 = 0.133

1/3 × 3/10 = 0.1

1/3 × 2/10 = 0.067

1/3 × 1/10 = 0.033

1/3 × 0/10 = 0

TOTAL = 0.333