A red die and a blue die are thrown time. List all the possible outcomes in a systematic at the same way.
Find -the probability of obtaining
(a) A total of 10,
(b) a total of 12,
(c) a total less than 6
(d) (the same number of both dice
(e) a total more than 9
What is the most likely total?
Answers
Step-by-step explanation:
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A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability:
(i) that the sum of the two numbers that turn up is 8
(ii) of obtaining a total 6
(iii) of obtaining a total of 10
(iv) of obtaining the same number on both dice
(v) of obtaining a total of more than 9
(vi) that the sum of the two numbers appearing on the top of the dice is 13
(vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12
(viii) that the product of numbers appearing on the top of the dice is less than 9
(ix) that the difference of the numbers appearing on the top of the two dice is 2
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Solution
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In a throw of pair of dice - white and black, total no of possible outcomes=36(6×6) which 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)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
Solution (i):
Let E be event of getting the sum as 8
No. of favorable outcomes =5 (i.e.,(2,6),(3,5),(4,4),(5,3),(6,2))
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
36
5
Solution (ii):
Let E be event of obtaining the total 6
No. of favorable outcomes =5 (i.e.,(1,5),(2,4),(3,3),(4,2),(5,1))
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
36
5
Solution (iii):
Let E be event of obtaining the total 10
No. of favorable outcomes =3 (i.e.,(4,6),(5,5),(6,4))
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
36
3
=
12
1
Solution (iv):
Let E be event of getting the same number on both dice
No. of favorable outcomes =6 (i.e.,(1,1),(2,2),(3,3),(4,4),(5,5),(6,6))
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
36
6
=
6
1