## Chapter 33 – Probability Exercise Ex. 33.1

An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

In this experiment, a coin is tossed and if the outcome is tail then a die is tossed once.

Otherwise, the coin is tossed again.

The possible outcome for coin is either head or tail.

The possible outcome for die is 1,2,3,4,5,6.

If the outcome for the coin is tail then sample space is S1={(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

If the outcome is head then the sample space is S2={(H,H),(H,T)}

Therefore the required sample space is S={(T,1),(T,2),(T,3),(T,4),(T,5),(T,6),(H,H),(H,T)}

In a random sampling, three items are selected so it could be any of the following:

a) All defective or

b) All non-defective or

c) Combination of defective and non defective.

Sample space associated with this experiment is

S={DDD, NDN, DND, DNN, NDD, DDN, NND, NNN}

In this experiment, a die is rolled. If the outcome is 6 then experiment is over. Otherwise, die will be rolled again and again.

## Chapter 33 – Probability Exercise Ex. 33.2

A card is picked up from a deck of 52 playing cards.

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

(ii) What is the event that the chosen card is back faced card?

## Chapter 33 – Probability Exercise Ex. 33.3

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:

(i) All the three balls are white

(ii) All the three balls are red

(iii) One ball is red and two balls are white.

## Chapter 33 – Probability Exercise Ex. 33.4

Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?