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).
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).