NCERT Class 11-Math's: Exemplar Chapter –16 Probability Part 6

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Question 14:

If are three mutually exclusive and exhaustive events of an experiment such that

is equal to

(A)

(B)

(C)

(D)

Answer:

(B) Is the correct answer. Let which gives

Now since A, B, C are mutually exclusive and exhaustive events, we have

Question 15:

One mapping (function) is selected at random from all the mappings of the set into itself. The probability that the mapping selected is one to one is

(A)

(B)

(C)

(D) None of these

Answer:

(C) Is the correct answer. Total number of mappings from a set having elements onto itself is

Now, for one to one mapping the first element in A can have any of the n images in A; the element in A can have any of the remaining images, counting like this, the nth element in A can have only image.

Therefore, the total number of one to one mappings is .

Hence the required probability is

16.3 EXERCISE

Short Answer Type

Question 1:

If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?

Answer:

Question 2:

Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?

[Hint: First find the probability that the couple has adjacent desks, and then subtract it from 1.]

Answer:

Question 3:

Suppose an integer from through is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of .

Answer:

Question 4:

An experiment consists of rolling a die until a appears.

(i) How many elements of the sample space correspond to the event that the 2 appears on the roll of the die?

(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the roll of the die?

[Hint:(a) First rolls have outcomes each and rolls should result in 1 outcomes. (b)

Answer:

(a) elements

(b)

Question 5:

A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find , where is the event that a number greater than 3 occurs on a single roll of the die.

Answer:

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