Advertisements
Advertisements
Question
The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.
Solution
Sample space,
S = {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5),
(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5),
(2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),
(3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),
(4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5),
(5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)}
∴ n(S) = 36
Let A be the event that the product of digits on the upper face is zero.
∴ A = {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0)}
∴ n(A) = 11
∴ P(A) = `("n"("A"))/("n"("S"))`
∴ P(A) = `11/36`
APPEARS IN
RELATED QUESTIONS
There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one girl
Event B: The committee contains one boy and one girl
Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.
P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.
A bag contains, white, black and red balls only. A ball is drawn at random from the bag.If the probability of getting a white ball is 3/10 and that of a black ball is 2/5 then find the
probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is
`(A)4/15`
`(B)2/15`
`(C)1/5`
`(D)1/3`
All red face cards are removed from a pack of playing cards. The remaining cards were well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is
(i) a red card
(ii) a face card
(iii) a card of clubs
A Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest.
Which of the above values you prefer more?
A box contains 5 red marbels, 8 white marbles and 4 green marbles, One marble is taken out of the box at ramdom. What is the probability that the marble taken out will be white?
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person form the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is extremely patient
A piggy bank contains hundred 50 paise coins, fifity ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell will be of value more than ₹1
In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 are blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of green
Two coins are tossed simultaneously. Find the probability of getting exactly one head.
In the probability that the digit is a multiple of 3 is
If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the numbers 1, 4, 9. Then, P(xy < 9)
What is the probability that a non-leap year has 53 Sundays?
17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears an odd number.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting a red face card.
Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is not a perfect square number.
A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a composite number between 50 and 70.
A die is thrown once. Find the probability of getting.
(a) a prime number.
(b) an odd number
A coin is tossed twice. Find the probability of getting: exactly one head
