Question

Which theoretical probabilities are equal to 1/3? Check all that apply.

rolling an even number on the first roll

landing on a star space on the first roll

landing at Cat Town on the first roll

not landing on a question mark or star on the first roll

rolling a number greater than 4 on the first roll

Answer 1

Assuming your rolling a six sided die, then the answers should be all of these:

landing on a star space on the first roll

not landing on a question mark or star on the first roll

rolling a number greater than 4 on the first roll

Answer 2

2nd 4th and 5th theoretical probabilities are equal to 1/3.

Explanation:

If a dice with six faces, having numbers (1-6) on each face is being rolled.

We will use the formula

`P=\frac{\text{favorable outcome}}{\text{total number of possible outcomes}}`

(1) rolling an even number on the first roll.

Favorable outcome = 2,4,6 (3 numbers)

`P=(3)/(6)=(1)/(2)`

(2) Landing on a star space on the first roll.

Maximum numbers of stars to be reached in first roll = 2

`P=(2)/(6)=(1)/(3)`

(3) Landing at Cat Town on the first roll is not possible because it is at 9th place. and we can reach at 6 place on first roll only.

Therefore,
`P=(0)/(6)` =0

(4) Not landing on a question mark or star on the first roll.

Only 1 and 2 place has not question mark or star out of 6 places.

Favorable outcome will be = 2 (1 and 2)

`P=(2)/(6)=(1)/(3)`

(5) Rolling a number greater than 4 on the first roll.

Favorable outcome = 2 ( 5 and 6)

`P=(2)/(6)=(1)/(3)`

Therefore, 2nd 4th and 5th theoretical probabilities are equal to 1/3.