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

Explanation:

Step1: Count total number of spaces

There are 37 spaces on the game - board. Probability of an event $E$ is given by $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Analyze "rolling an even number on the first roll"

Assuming a standard die - roll context (not clear from the image but if we consider a die roll related to movement), a standard die has 6 sides. The number of even numbers on a die is 3. But we don't know the relation between die - roll and the game - board movement clearly. However, if we assume the die roll determines the movement and we consider the game - board, the number of favorable outcomes for rolling an even number and landing on a space is not such that the probability is $\frac{1}{37}$.

Step3: Analyze "landing on a star space on the first roll"

Count the number of star spaces. If there is 1 star space out of 37 total spaces, the probability of landing on a star space on the first roll is $P=\frac{1}{37}$.

Step4: Analyze "landing at Cat Town on the first roll"

If Cat Town is 1 space out of 37 total spaces, the probability of landing at Cat Town on the first roll is $P = \frac{1}{37}$.

Step5: Analyze "not landing on a question mark or star on the first roll"

Count the number of non - question - mark and non - star spaces. If the number of non - question - mark and non - star spaces is not 1 out of 37, the probability is not $\frac{1}{37}$.

Step6: Analyze "rolling a number greater than 4 on the first roll"

On a standard 6 - sided die, the numbers greater than 4 are 5 and 6 (2 numbers). The probability of rolling a number greater than 4 on a die is $\frac{2}{6}=\frac{1}{3}$, and its relation to the 37 - space game - board doesn't make the probability $\frac{1}{37}$.

Answer:

landing on a star space on the first roll, landing at Cat Town on the first roll