### Probability

EXERCISE - 4.1

1. In a each of the following experiments write the sample space S, number of sample points n (S), events P, Q, R using set and n (P), n (Q) and n (R). Find the events among the events defined above which are : complementary events, mutually exclusive events and exhaustive events.

(i) Three coins are tossed simultaneously :
P is the event of getting at least two heads.
Q is the event of getting no head.
R is the event of getting head on second coin. [Ans + VIDEO.]

(ii) A die is thrown :
P is the event of getting an odd number.
Q is the event of getting an even number.
R is the event of getting a prime number. [Ans+VIDEO.]

(iii) Two dice are thrown :
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same score on both dice. [Ans + VIDEO.]

(iv) There are 3 red, 3 white and 3 green balls in a bag. One ball is drawn at random from a bag :
P is the event that ball is red.
Q is the event that ball is not green.
R is the event that ball is red or white. [Ans + VIDEO.]

(v) Form two digit numbers using the digits 0, 1, 2, 3, 4, 5 without repeating the digits.
P is the event that the number so formed is even.
Q is the event that the number so formed is divisible by 3.
R is the event that the number so formed is greater than 50. [Ans + VIDEO.]

(vi) A coin is tossed and a die is thrown simultaneously :
P is the event of getting head and a odd number.
Q is the event of getting either H or T and an even number.
R is the event of getting a number on die greater than 7 and a tail. [Ans+VIDEO.]

(vii) There are 3 men and 2 women. A ‘Gramswachaatta Abhiyan’ committee of two is to be formed.
P is the event that the committee should contain at least one woman.
Q is the event that the committee should contain one man and one woman.

R is the event that there is not woman in the committee.  [Ans. VIDEO]

EXERCISE - 4.2

1. If two coins are tossed then find the probability of the events :
(i) at least one tail turns up
(iii) at the most one tail turns up  [Ans.]

2. A coin is tossed three times then find the probability of

(i) getting head on middle coin

(ii) getting exactly one tail

(iii) getting no tail [Ans.]

3. A die is thrown then find the probability of getting

(i) an odd number

(ii) a perfect square

(iii) a number greater than 3 [Ans.]

4. Two dice are thrown find the probability of getting :

(i) The sum of the numbers on their upper faces is divisible by 9.

(ii) The sum of the numbers on their upper faces is at most 3.

(iii) The number on the upper face of the first die is less than the number on the upper face of the second die. [Ans.]

5. A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box. What is the probability that number on the card is

(i) a prime number

(ii) perfect square

(iii) multiple of 5   [Ans.]

6. Two digit number are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. Find the probability of the events that :

(i) the number formed is an even number.

(ii) the number formed is greater than 40.

(iii) the number formed is prime number. [Ans.]

7. There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains :

(i) at least one girl

(ii) one boy and one girl

(iii) only boys [Ans.]

8. If a card is drawn from a pack of 52 cards. Find the probability of getting:

(i) a black card

(ii) not a black card

(iii) a card bearing number between 2 to 5 including 2 and 5    [Ans.]

9. A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is :