Question

Two different dice are tossed together.find the probability.(1)of geeting a doublet (2)of getting a sum of 10,t he number less on the two dice

Answer 1

A die has 6 faces marked as 1,2, 3, 4, 5, 6. When we throw a die , than total number of outcomes = 6 { 1 , 2 , 3 , 4 , 5 , 6 }
But when we throw two dice simultaneously , than total number of outcomes = 6² = 6 × 6 = 36
Total possible outcomes on throwing two dice 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)}
Number of all possible outcomes=36

SOLUTION:

i)Total number of outcomes= 36
Favourable outcomes are : (1,1),(2,2) ,(3,3),(4,4),(5,5),(6,6)
Number of outcomes favourable = 6
Probability = Number of favourable outcomes / Total number of outcomes.
Required probability = P(getting the doublet) = 6/36 = ⅙
Hence, the probability of getting the doublet = ⅙.

ii)Total number of outcomes= 36
Favourable outcomes are : (5,5),(4,6) ,(6,4)
Number of outcomes favourable = 3
Probability = Number of favourable outcomes / Total number of outcomes.
Required probability = P(getting the sum on both the die as 10) = 3 /36 = 1/12
Hence, the probability of getting the sum on both the die as 10 = 1/12.

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Answer 2

Given:

Two dice

To find:

The probability of getting a double

The probability of getting a sum of 10

Solution:

Sample space = ( 1, 0 ), ( 1, 1 ), ( 1, 2 )... ( 6, 6 )

Hence,  

Sample space = 36

To find the probability of getting a doublet,

Outcomes = ( 1, 1 ), ( 2, 2 ).. ( 6, 6 )

Possible outcomes = 6

P (getting a double) = 6 / 36  

Hence, P (getting a double) = 1 / 6

To find the probability of getting a sum of 10,

Possible outcomes = ( 4, 6 ), ( 6, 4 ), ( 5, 5 )  

P (getting a sum of 10 ) =3/36

Hence, P ( getting a sum of 10 ) = 1 / 12

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