Advertisements
Advertisements
Question
A fair die is thrown two times. Find the probability that the product of numbers on them is 12.
Solution
When a fair die is tossed twice, the sample sp ace S is given by
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
∴ n (S) = 36
Let D = the event that product of numbers is 12
∴ D = {(2, 6), (3, 4), (4, 3), (6, 2)}
∴ n(D) = 4
∴ P(D) = `("n"("D"))/("n"("S"))`
= `4/36`
= `1/9`
APPEARS IN
RELATED QUESTIONS
A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8
A fair die is thrown two times. Find the probability that the first throw gives a multiple of 2 and the second throw gives a multiple of 3.
Two cards are drawn from a pack of 52 cards. Find the probability that one is a face card and the other is an ace card
Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit.
Three cards are drawn from a pack of 52 cards. Find the chance that at least one is a diamond card
Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, without replacement
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement O is at the begining and end with T
15 professors have been invited for a round table conference by Vice chancellor of a university. What is the probability that two particular professors occupy the seats on either side of the Vice chancellor during the conference
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that one is black and two are red.
A bag contains 5 red, 4 blue and an unknown number m of green balls. If the probability of getting both the balls green, when two balls are selected at random is `1/7`, find m
Form a group of 4 men, 4 women and 3 children, 4 persons are selected at random. Find the probability that, exactly 2 men are selected
A number is drawn at random from the numbers 1 to 50. Find the probability that it is divisible by 2 or 3 or 10
Select the correct option from the given alternatives :
There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is
Select the correct option from the given alternatives :
Two friends A and B apply for a job in the same company. The chances of A getting selected is `2/5` and that of B is `4/7`. The probability that both of them get selected is
Select the correct option from the given alternatives :
The probability that a student knows the correct answer to a multiple choice question is `2/3`. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is `1/4`. Given that the student has answered the question correctly, the probability that the student knows the correct answer is
Solve the following:
A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2, .......6. What is the probability, in one roll of the die, that an odd number of dots will turn up?
Solve the following:
An urn contains 5 red balls and 2 green balls. A ball is drawn. If its green, a red ball is added to the urn and if its red, a green ball is added to the urn. (The original ball is not returned to the urn). Then a second ball is drawn. What is the probability that the second ball is red?
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls
Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is ______.
A coin is tossed 9 times. The probability of obtaining at most one head is ______
If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is ______.
The probability that three cards drawn from a pack of 52 cards, all are red is ______.
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is ______.
A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is ______.
Four mangoes and five apples are in a box. If two fruits are chosen at random, then find the probability that one is a mango and other is an apple ______.
If two letters of the word MOTHER are selected at random. Probability that both are consonants is ______.
Let f(x) = `{{:(1/x^2",", 1 < x < oo"," "be the p.d.f of"),(0",", "otherwise"):}`
a r.v. X. If C1 = {x : 1 < x <2} and C2 = {x : 4 < x < 5}, then P(C1 ∪ C2) =______.
In a simultaneous toss of five coins, the probability of getting exactly four tails is ______.
A die is rolled. If X denotes the number of positive divisors of the outcome then the range of the random variable X is ______.
Probability that a person will develop immunity after vaccinations is 0.8. if 8 people are given the vaccine, then probability that all develop immunity is = ______.
