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Answers
Solution!
We have to calculate the probability of the events given in the question when two dice are thrown simultaneously. We know that probability is the ratio of favourable outcomes and all possible outcomes. Mathematically,
Probability = Favourable outcomes ÷ All possible outcomes
All possible outcomes when two dice are rolled are 36.
(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)
(a) P(an odd number as a sum)
Answer:- 1/2
Explanation:-
3 → (1,2),(2,1)
5 → (2,3),(3,2),(1,4),(4,1)
7 → (1,6),(6,1),(2,5),(5,2),(3,4),(4,3)
9 → (3,6)(6,3),(4,5),(5,4)
11 → (5,6),(6,5)
All possible outcomes = 36
Favourable outcomes = 18
Probability = 18/36
Probability = 1/2
(b) P(sum as a prime number)
Answer:- 5/12
Explanation:-
2 → (1,1)
3 → (1,2),(2,1)
5 → (2,3),(3,2),(1,4),(4,1)
7 → (1,6),(6,1),(2,5),(5,2),(3,4),(4,3)
11 → (5,6),(6,5)
All possible outcomes = 36
Favourable outcomes = 15
Probability = 15/36
Probability = 5/12
(c) P(a doublet of odd numbers)
Answer:- 1/12
Explanation:-
(1,1),(3,3),(5,5)
All possible outcomes = 36
Favourable outcomes = 3
Probability = 3/36
Probability = 1/12
(d) P(a total of atleast 9)
Answer:- 5/18
Explanation:- The total should atleast be 9. It can be more than 9 but not less than 9.
9 → (3,6)(6,3),(4,5),(5,4)
10 → (5,5),(4,6),(6,4)
11 → (5,6),(6,5)
12 → (6,6)
All possible outcomes = 36
Favourable outcomes = 10
Probability = 10/36
Probability = 5/18
(e) P(a multiple of 5 as a sum)
Answer:- 7/36
Explanation:-
5 → (2,3),(3,2),(1,4),(4,1)
10 → (5,5),(4,6),(6,4)
All possible outcomes = 36
Favourable outcomes = 7
Probability = 7/36
(f) P(a doublet)
Answer:- 1/6
Explanation:-
(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
All possible outcomes = 36
Favourable outcomes = 6
Probability = 6/36
Probability = 1/6
(g) P(a multiple of 2 as a sum)
Answer:- 1/2
Explanation:-
2 → (1,1)
4 → (2,2),(1,3),(3,1)
6 → (1,5),(5,1),(2,4),(4,2),(3,3)
8 → (2,6),(6,2),(3,5),(5,3),(4,4)
10 → (5,5),(4,6),(6,4)
12 → (6,6)
All possible outcomes = 36
Favourable outcomes = 18
Probability = 18/36
Probability = 1/2
(h) P(getting the sum 9)
Answer:- 1/9
Explanation:-
9 → (3,6)(6,3),(4,5),(5,4)
All possible outcomes = 36
Favourable outcomes = 4
Probability = 4/36
Probability = 1/9
(i) P(getting a sum greater than 12)
Answer:- 0
Explanation:- The greatest combination can be (6,6) whose sum is the greatest possible outcome 12. So, it isn't possible to get a sum greater than 12.
All possible outcomes = 36
Favourable outcomes = 0
Probability = 0/36
Probability = 0
(j) P(a prime number on each die)
Answer:- 1/4
Explanation:-
(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)
All possible outcomes = 36
Favourable outcomes = 9
Probability = 9/36
Probability = 1/4
(k) P(a multiple of 2 on one die and a multiple of 3 on other die)
Answer:- 11/36
Explanation:-
(2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(3,4),(3,6),(6,2),(6,4)
All possible outcomes = 36
Favourable outcomes = 11
Probability = 11/36