pls answer it, probability only. 100 points
in two dice game, the player take turns to roll both dice, they can roll as many times as they want
in one turn. A player scores the sum of the two dice thrown and gradually reaches a higher score as
they continue to roll. If a single number 1 is thrown on either die, the score for that whole turn is
lost. Two dice are thrown simultaneously
37. What is the probability of getting the sum as an even number ?
(i) ¾ (ii) 1/2 (iii) 1/4 (iv) 5/8
38. What is the probability of getting the sum as a prime number ?
(i) 5/12 (ii) 1/6 (iii) 7/12 (iv) 11/12
39. What is the probability of getting the sum of at least 10?
(i) 5/12 (ii) 5/6 (iii) 1/6 (iv) 7/12
40. What is the probability of getting a doublet of even number ?
(i) 1/12 (ii) 5/12 (iii) 11/12 (iv) 7/12
41. What is the probability of getting a product of numbers greater than 16?
(i) 7/36 (ii) 2/9 (iii) 1/4 (iv) 11/36
2
Answers
Simple machine, any of several devices with few or no moving parts that are used to modify motion and the magnitude of a force in order to perform work. They are the simplest mechanisms known that can use leverage (or mechanical advantage) to increase force.
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
=
3
1