Question

If two dice are rolled one time find the probability
A 3 on one die or both dice

Answer 1

`|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=(11)/(36)\approx30.6\%`

Answer 2

`P=(13)/(36)=0.361`

Explanation:

There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is

`P = (1)/(6)`.

When throwing the two dice together, the probability of obtaining a 3 is the same:

`P_1 = (1)/(6) * (5)/(6) + (5)/(6) * (1)/(6)=(5)/(18)`

Since the events are independent then the probability of obtaining a three in both dice is:

`P_2 = (1)/(6) * (1)/(6) = (1)/(12)`.

Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities
`P_1` and
`P_2`

`P=(1)/(12)+(5)/(18)=(13)/(36)=0.361`