Question

You roll a fair number cube. Find each probability:

2. P(2, then 2)

1. P(3, then 5)

3. P(4, then odd)

Answer 1

P(2, then 2) =
`(1)/(36)`

P(3, then 5) =
`(1)/(36)`

P(4, then odd) =
`(1)/(12)`

Explanation:

Given: A fair number cube is rolled

To find: P(2, then 2) , P(3, then 5) , P(4, then odd)

Solution:

Probability refers to chances of occurrence of some event.

Probability = Number of favourable outcomes/Total number of outcomes

Sample space =
`\left \{ 1,2,3,4,5,6 \right \}`

Total number of outcomes = 6

P(2, then 2) = P(2)P(2) =
`(1)/(6)((1)/(6))=(1)/(36)`

P(3, then 5) = P(3)P(5) =
`(1)/(6)((1)/(6))=(1)/(36)`

Odd numbers out of the sample space =
`\left \{ 1,3,5 \right \}`

P(4, then odd) = P(4)P(odd) =
`((1)/(6))((3)/(6) )=(1)/(12)`