Question

In a game, if you roll a 2 or a 3 on a 6-sided number cube, you lose a turn. NOTE: This is just using one number cube. a. What is the probability that you roll a 2 or 3, P (2 or 3)? Explain your reasoning. (2 points possible) b. What is the probability that you don’t roll a 2 or a 3, P (NOT a 2 or 3)? Explain your reasoning.

Answer 1

(a)1/3

(b)2/3

Explanation:

This is a 6-sided number cube, therefore total possible outcomes, n(S)=6

(a)Probability of rolling a 2 OR 3 =P(2)+P(3)

`=(1)/(6) +(1)/(6) =(2)/(6)\\= (1)/(3)`

(b)Probability of not rolling a 2 OR 3

In probability, the sum of the probability of an event and its complement is always 1.

Therefore:

P(Rolling a 2 or 3)+P(Not rolling a 2 or 3)=1

From part (a) above:

Probability of rolling a 2 OR 3=
`(1)/(3)`

Therefore:

`(1)/(3)+$P(Not rolling a 2 or 3)=1\\P(Not rolling a 2 or 3)=1-(1)/(3)=(2)/(3)`