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Chapter 15: Q9P (page 724)

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鈥檚 and 7 B鈥檚. 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

Expert verified

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

01

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.

02

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 鈥�(i)

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

P = 3/10

03

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.

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Most popular questions from this chapter

Given a family of two children (assume boys and girls equally likely, that is, probability for each), what is the probability 1/2 that both are boys? That at least one is a girl? Given that at least one is a girl, what is the probability that both are girls? Given that the first two are girls, what is the probability that an expected third child will be a boy?

Two dice are thrown. Given the information that the number on the first die iseven, and the number on the second is <4, set up an appropriate sample space andanswer the following questions.

(a) What are the possible sums and their probabilities?

(b) What is the most probable sum?

(c) What is the probability that the sum is even?

Consider the set of all permutations of the numbers 1, 2, 3. If you select a permutationat random, what is the probability that the number 2 is in the middle position?In the first position? Do your answers suggest a simple way of answering the same questions for the set of all permutations of the numbers 1 to 7?

A card is selected from a shuffled deck. What is the probability that it is either a king or a club? That it is both a king and a club?

(a) There are 3 red and 5 black balls in one box and 6 red and 4 white balls in another. If you pick a box at random, and then pick a ball from it at random, what is the probability that it is red? Black? White? That it is either red or white?

(b) Suppose the first ball selected is red and is not replaced before a second ball

is drawn. What is the probability that the second ball is red also?

(c) If both balls are red, what is the probability that they both came from the same box?
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