Question

In a chemical plant, 24 holding tanks are used for final product storage. Suppose that six of the tanks contain high viscosity material. Four tanks are selected at random and without replacement. What is the probability that exactly one tank in the sample contains high-viscosity material

Answer 1

The probability is 0.461

Explanation:

Since six tanks contain high viscosity material, it means that 18 does not contain since the total number of tanks is 24.

Now, here, we know that we are selecting a total of 4 tanks.

out of the tanks with high viscosity materials, we will be selecting one only while out of the others without viscosity materials we shall need selecting three.

Thus,

the number of ways we can select one tank with viscosity material from a total of six tanks will be 6C1 = 6 ways

Now, we want to select three from the remaining 18 tanks

The number of ways we can do this is 18C3 = 816 ways

Finally, we are selecting 4 out of 24 tanks.

The number of ways we can do this is 24C4 = 10,626 ways

Now, we proceed to calculate the probability.

Kindly note that we are selecting 1 from 4 and 3 from 18

The term ‘and’ in probability means we are multiplying the probabilities of these events together and thus, that means that we are going to combine our numbers of selections.

So the total number of ways in which we can select 1 out of 3 and 3 out of 18 will be = 6 * 816 = 4,896 ways

The probability would now be 4896/10626 = 0.461