Question

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die and 5 on red die). (Enter your answer as a fraction.) (c) Find P(5 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)). (Enter your answer as a fraction.)

Answer 1

a

Yes

b

`P(1 \& 5) = (1)/(36)`

c

`P(5 \& 1) = (1)/(36)`

d

`P(5 \& 1 | 1\& 5 ) = (1)/(18)`

Explanation:

From the question we are told that

Two fair dice, one green and one red were rolled

Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the probability of getting a 1 on a dice rolled is
`P(1) = (1)/(6)`

the probability of getting a 5 on a dice rolled is
`P(5) = (1)/(6)`

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

`P(1 \& 5) = (1)/(6) *(1)/(6)`

`P(1 \& 5) = (1)/(36)`

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

`P(5 \& 1) = (1)/(6) *(1)/(6)`

`P(5 \& 1) = (1)/(36)`

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

`P(5 \& 1 | 1\& 5 ) = (1)/(36) + (1)/(36)`

`P(5 \& 1 | 1\& 5 ) = (1)/(18)`