Question

You are trying to find instrument A in a laboratory. Unfortunately, someone has put both instruments A and another kind (which we shall call B) away in identical unmarked boxes mixed at random on a shelf. You know that the laboratory has 3 A’s and 7 B’s. If you take down one box, what is the probability that you get an A? If it is a B and you put it on the table and take down another box, what is the probability that you get an A this time?

Short answer

The probability that box selected is A is 3/10.

The probability that when a box is selected at random and it is B and kept aside, the probability that you get an A in second selection is 1/3.

Step-by-step solution

Definition of Mutually exclusive events

The events in a particular experiment that cannot occur at the same point of time are termed as Mutually exclusive events. For instance, when a coin is tossed, head and tail cannot appear at the same point of time.

Determination of the probability that box selected is A

There is total 3 A and 7 B boxes. This implies that there is total 10 boxes with each being mutually exclusive from which A box is to be selected.

This implies that the number of outcomes favourable are 3 and total number of outcomes are 10.

Write the expression for the probability.

P = number of outcomes favorable to E/total number of outcomes …(i)

Substitute the values in the above expression to find the probability that box selected is A.

P = 3/10

Determination of the probability that when a box is selected at random and it is B and kept aside, the probability that you get an A in second selection

When the first box is selected and it is B, it is kept aside. For the second selection, there are total 3 A and 6 B boxes, this implies that there are total 9 boxes with each being mutually exclusive from which A box is to be selected.

This implies that the number of outcomes favourable are 3 and total number of outcomes are 9.

Substitute the values in the equation (i) to find the probability thatwhen a box is selected at random and it is B and kept aside, the probability that you get an A in second selection.

P = 3/9

=1/3

Thus, the probability that box selected is A is 3/10, and the probability thatwhen a box is selected at random and it is B and kept aside, the probability that you get an A in second selection is 1/3.