In a single throw of two dice, find the probability of :
(i) a doublet
(ii) a number less than 3 on each dice
(iii) an odd number as a sum
(iv) a total of atmost 10
(v) an odd number on one dice and a number less than or equal to 4 on other dice.

Question

In a single throw of two dice, find the probability of :
(i) a doublet
(ii) a number less than 3 on each dice
(iii) an odd number as a sum
(iv) a total of atmost 10
(v) an odd number on one dice and a number less than or equal to 4 on other dice.

KnowledgeBoat · Accepted Answer

When two dice are rolled simultaneously; Total number of possible outcomes = 6 × 6 = 36. (i) For obtaining a doublet, the favourable outcomes are : (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6). ∴ Number of favourable outcomes = 6 P(getting a doublet) = . Hence, the probability of getting a doublet = . (ii) For obtaining a number less than 3 on each dice, the favourable outcomes are : (1, 1), (1, 2), (2, 1), (2, 2). ∴ Number of favourable outcomes = 4 P(getting a number less than 3 on each dice) = . Hence, the probability of getting a number less than 3 on each dice = . (iii) For obtaining an odd number as a sum, the favourable outcomes are : (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). ∴ Number of favourable outcomes = 18 P(getting an odd number as a sum) = . Hence, the probability of getting an odd number as the sum = . (iv) For obtaining a total of atmost 10, the favourable outcomes are : (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), (6, 1), (6, 2), (6, 3), (6, 4). ∴ Number of favourable outcomes = 33 P(getting a total of atmost 10) = . Hence, the probability of getting a total of atmost 10 = . (v) For obtaining an odd number on one dice and a number less than or equal to 4 on other dice, the favourable outcomes are : (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 3), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 1), (4, 3), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4). ∴ Number of favourable outcomes = 20 P(getting an odd number on one dice and a number less than or equal to 4 on other dice) = . Hence, the probability of getting an odd number and a number less than or equal to 4 on other dice = .

Mathematics

In a single throw of two dice, find the probability of :
(i) a doublet
(ii) a number less than 3 on each dice
(iii) an odd number as a sum
(iv) a total of atmost 10
(v) an odd number on one dice and a number less than or equal to 4 on other dice.

Probability

Related Questions

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is :
(i) a red card
(ii) a black card
(iii) a spade
(iv) an ace
(v) a black ace
(vi) ace of diamonds
(vii) not a club
(viii) a queen or a jack.

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is :
(i) a multiple of 4 or 6.
(ii) a multiple of 3 and 5.
(iii) a multiple of 3 or 5.

Mathematics

In a single throw of two dice, find the probability of :(i) a doublet(ii) a number less than 3 on each dice(iii) an odd number as a sum(iv) a total of atmost 10(v) an odd number on one dice and a number less than or equal to 4 on other dice.

Probability

Related Questions

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is :(i) a red card(ii) a black card(iii) a spade(iv) an ace(v) a black ace(vi) ace of diamonds(vii) not a club(viii) a queen or a jack.

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is :(i) a multiple of 4 or 6.(ii) a multiple of 3 and 5.(iii) a multiple of 3 or 5.

In a single throw of two dice, find the probability of :
(i) a doublet
(ii) a number less than 3 on each dice
(iii) an odd number as a sum
(iv) a total of atmost 10
(v) an odd number on one dice and a number less than or equal to 4 on other dice.

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is :
(i) a red card
(ii) a black card
(iii) a spade
(iv) an ace
(v) a black ace
(vi) ace of diamonds
(vii) not a club
(viii) a queen or a jack.

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is :
(i) a multiple of 4 or 6.
(ii) a multiple of 3 and 5.
(iii) a multiple of 3 or 5.