Login/Sign Up
Home » In a single throw of two dice, find the probability of
In a single throw of two dice, find the probability of (ii)getting a doublet of odd numbers
(iii)getting the sum as a prime number
CBSE | Class 11 | Exercise 31A | Guides | Maths | Probability Distribution | RS Aggarwal
In a single throw of two dice, find the probability of (ii)getting a doublet of odd numbers
(iii)getting the sum as a prime number
  • Answer : (i) We know that,

Probability of occurrence of an event

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),Outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 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 no.of outcomes are 36

In that only (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1) are our

desired outputs as there sum is less than 6 Therefore no.of desired outcomes are 10

Therefore, the probability of getting a sum less than 6

Conclusion: Probability of getting a sum less than 6, when two dice are rolled is 5/18

  • We know that,

Probability of occurrence of an event

Total doublets are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)In (a, b) if a=b then it is called a doublet

In (a, b) if a=b and if a, b both are odd then it is called a doublet Odd doublets are (1, 1), (3, 3), (5, 5)

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), (5, 6) ,

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Conclusion: Probability of getting doublet of odd numbers, when two dice are rolled is 1/12
Total no.of outcomes are 36 and desired outcomes are 3 Therefore, probability of getting doublet of odd numbers

  • We know that,

Probability of occurrence of an event


(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),Outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 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 no.of outcomes are 36

Desired outputs are (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1),

(4, 3), (5, 2), (5, 6), (6, 1), (6, 5)

Total no.of desired outputs are 15

Therefore, probability of getting the sum as a prime number

Conclusion: Probability of getting the sum as a prime number, when two dice are rolled is 5/12

i

More Material