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Asap fast no spammingtwo dice are thrown simultaneously find the probability of getting the sum of two numbers on the dice is greater than 6 but less than 9 |
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Answer»
Sample space for total NUMBER of possible outcomes (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) Total number of outcomes =36 (i) Favorable outcomes for sum as prime are (1,1),(1,2),(1,4),(1,6),(2,3),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5) Number of favorable outcomes =15 Hence, the probability of getting the sum as a prime number. = 36 15
= 12 5
(ii) Favorable outcomes for total of atleast 10 are (4,6),(5,5),(5,6),(6,4),(6,5),(6,6) Number of favorable outcomes =6 Hence, the probability of getting a total of atleast 10 = 36 6
= 6 1
(iii) Favorable outcomes for a doublet of even number are (2,2),(4,4),(6,6) Number of favorable outcomes =3 Hence, the probability of getting a doublet of even number = 36 3
= 13 1
(IV) Favorable outcomes for a multiple of 2 on one dice and a multiple of 3 on the other dice are (2,3),(2,6),(3,2),(3,4),(3,6),(4,3),(4,6),(6,2),(6,3),(6,4),(6,6) Number of favorable outcomes =11 Hence, the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice = 36 11
(v) Favorable outcomes for getting a multiple of 3 as the sum (1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3)(6,6) Number of favorable outcomes =12 Hence, the probability of getting a multiple of 3 as the sum = 36 12
= Sample space for total number of possible outcomes (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) Total number of outcomes =36 (i) Favorable outcomes for sum as prime are (1,1),(1,2),(1,4),(1,6),(2,3),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5) Number of favorable outcomes =15 Hence, the probability of getting the sum as a prime number. = 36 15
= 12 5
(ii) Favorable outcomes for total of atleast 10 are (4,6),(5,5),(5,6),(6,4),(6,5),(6,6) Number of favorable outcomes =6 Hence, the probability of getting a total of atleast 10 = 36 6
= 6 1
(iii) Favorable outcomes for a doublet of even number are (2,2),(4,4),(6,6) Number of favorable outcomes =3 Hence, the probability of getting a doublet of even number = 36 3
= 13 1
(iv) Favorable outcomes for a multiple of 2 on one dice and a multiple of 3 on the other dice are (2,3),(2,6),(3,2),(3,4),(3,6),(4,3),(4,6),(6,2),(6,3),(6,4),(6,6) Number of favorable outcomes =11 Hence, the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice = 36 11
(v) Favorable outcomes for getting a multiple of 3 as the sum (1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3) = 36 12
= 3 1
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