NCERT Class 11-Math's: Exemplar Chapter –16 Probability Part 3

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16.2 Solved Examples

Short Answer Type (S.A.)

Question 1:

An ordinary deck of cards contains cards divided into four suits. The red suits are diamonds and hearts and black suits are clubs and spades. The cards J, Q, and K are called face cards. Suppose we pick one card from the deck at random.

(a) What is the sample space of the experiment?

(b) What is the event that the chosen card is a black face card?

Answer:

(a) The outcomes in the sample space are cards in the deck.

(b) Let be the event that a black face card is chosen. The outcomes in E are Jack, Queen, King or spades or clubs. Symbolically

or

Question 2:

Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.

(a) List the eight elements in the sample space whose outcomes are all possible genders of the three children.

(b) Write each of the following events as a set and find its probability:

(i) The event that exactly one child is a girl.

(ii) The event that at least two children are girls

(iii) The event that no child is a girl

Answer:

(a) All possible genders are expressed as:

(b) (i)Let A denote the event : ‘exactly one child is a girl’

(ii) Let B denote the event that at least two children are girls.

(iii) Let denote the event: ‘no child is a girl’.

Question 3:

(a) How many two-digit positive integers are multiples of ?

(b) What is the probability that a randomly chosen two-digit positive integer is a multiple of ?

Answer:

(a) digit positive integers which are multiples of 3 are . Thus, there are such integers.

(b) digit positive integers are . Thus, there are 90 such numbers. Since out of these, 30 numbers are multiple of 3, therefore, the probability that a randomly chosen positive 2-digit integer is a multiple of 3, is

Question 4:

A typical PIN (personal identification number) is a sequence of any four symbols chosen from the 26 letters in the alphabet and the ten digits. If all PINs are equally likely, what is the probability that a randomly chosen PIN contains a repeated symbol?

Answer:

A PIN is a sequence of four symbols selected from symbols.

By the fundamental principle of counting, there are PINs in all. When repetition is not allowed the multiplication rule can be applied to conclude that there are

different PINs

The number of PINs that contain at least one repeated symbol

Thus, the probability that a randomly chosen PIN contains a repeated symbol is

Question 5:

An experiment has four possible outcomes A, B, C and D, that are mutually exclusive. Explain why the following assignments of probabilities are not permissible:

(a)

(b)

Answer:

(a) Since , this is not possible as for any event A.

(b)

This violates the condition that .

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