**OMTEX CLASSES**

**In each of the following experiments write the sample space S, number of sample points n(S), events P, Q, R using set form 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.**

**(6 marks)**

**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.**

**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.**

**Two dice are thrown find the probability of getting (3 marks)**

**The sum of the numbers on their upper faces is divisible by 9.**

**The sum of the numbers on their upper faces is at the most 3.**

**The number on the upper face of the first die is less than the number on the upper face of the second die.**

**A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box at random. What is the probability that the number on the card is (3 marks)**

**A prime number**

**Perfect square**

**Multiple of 5.**

**There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains. ( 3 marks)**

**At least one girl.**

**One boy and one girl.**

**Only boys.**

**One lottery ticket is drawn at random from a bag containing 20 tickets numbered from 1 to 20. Find the probability that the number on the ticket drawn is (4 marks)**

**Either even or square of an integer.**

**Divisible by 3 or 5.**

**In each of the following experiments write the sample space S, number of sample points n(S), events P, Q, R using set form 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.**

**(6 marks)**

**There are 3 red, 3 white and 3 green balls in a bag. One ball is drawn at random from the 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.**

**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.**

**A coin is tossed three times find the probability of getting (3 marks)**

**Getting head on middle coin.**

**Getting exactly one tail.**

**Getting no tail.**

**If a card is drawn from a pack of 52 cards. Find the probability of getting. (3 marks)**

**A black card.**

**Not a black card**

**A card bearing number between 2 to 5 including 2 and 5.**

**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 ( 3 marks)**

**The number formed is an even number.**

**The number formed is greater than 40.**

**The number formed is prime number.**

**Attempt the following questions. (4 marks)**

**If P(A) = 3/4, P(B’)=1/3 AND P(A∩B) = 1/2 then find P(A∪B).**

**A and B are two events on a sample space S such that P(A) = 0.8, P(B) = 0.6 and P(A∪B)= 0.9 find P(A∩B).**