**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**

**(ii) no head 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 :**

**(i) a spade**

**(ii) not of diamond**

**[Ans.]**