Question

When two dice are rolled, what is the probability that one die is a 4, given that the sum of the two dies is 9?

Answer 1

Answer:

There are 36 outcomes to rolling two dice. Your denominator will be a 36.

A four can be a 1-3, 2-2 or 3-1. That's 3 possibilities.

A nine can be made 3-6, 6-3, 4-5 or 5-4. That's 4 ways.

A twelve has only one outcome, both sixes.

The probability is 3+4+1 over 36. That's 8/36, simplified to 2/9.

Answer 2

Answer:

Total no. of outcomes when two dice are thrown 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)

Sum of $$10$ in pair of die can be:  

{(4,6),(5,5),(6,4)}

Outcome of sum of 10 is n(S)=3

Out of this those showing 4 are {(4,6),(6,4)} , n(E)=2

∴  Probability that one of the die showed 4.=  

3

2

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Step-by-step explanation: