Which theoretical probabilities are equal to 1/3? Check all that apply.
A. rolling an even number on the first roll
B. landing on a star space on the first roll
C. landing at Cat Town on the first roll
D. not landing on a question mark or star on the first roll
E. rolling a number greater than 4 on the first roll
Answer (2)
Count the total number of spaces on the board: 6.
Calculate the probability of landing on a star space: 6 1 .
Calculate the probability of landing at Cat Town: 6 1 .
Calculate the probability of not landing on a question mark or star: 6 4 = 3 2 .
Calculate the probability of rolling an even number: 6 3 = 2 1 .
Calculate the probability of rolling a number greater than 4: 6 2 = 3 1 .
The theoretical probability equal to 3 1 is rolling a number greater than 4. 3 1 .
Explanation
Analyze the problem Let's analyze the probabilities of each event to determine which are equal to 3 1 .
Count total spaces First, let's count the total number of spaces on the board. The spaces are START, ?, CAT, TOWN, END, and a star space. So there are 6 spaces in total.
Probability of landing on a star space Now, let's calculate the probability of landing on a star space. There is 1 star space out of 6 total spaces. So, the probability is 6 1 .
Probability of landing at Cat Town Next, let's calculate the probability of landing at Cat Town. There is 1 Cat Town space out of 6 total spaces. So, the probability is 6 1 .
Probability of not landing on a question mark or star Now, let's determine the number of spaces that are not question marks or stars. The spaces that are not question marks or stars are START, CAT, TOWN, and END. So there are 4 such spaces. The probability of not landing on a question mark or star is 6 4 = 3 2 .
Probability of rolling an even number Assuming a standard six-sided die is used, the probability of rolling an even number (2, 4, or 6) is 6 3 = 2 1 .
Probability of rolling a number greater than 4 Assuming a standard six-sided die is used, the probability of rolling a number greater than 4 (5 or 6) is 6 2 = 3 1 .
Compare probabilities and conclude Comparing each calculated probability to 3 1 , we find that only the probability of rolling a number greater than 4 is equal to 3 1 .
Examples
In a board game, calculating the probability of landing on certain spaces helps players understand their chances of success and make strategic decisions. For example, knowing the probability of landing on a space that awards extra points can influence a player's decision to take a certain path. Similarly, understanding the likelihood of encountering a penalty space can guide players to avoid risky routes. This concept extends to various real-life scenarios, such as assessing the risk of different investment options or predicting the outcome of a marketing campaign based on the probability of reaching a specific target audience.
The only theoretical probability equal to 3 1 among the given options is option E, which is rolling a number greater than 4 on the first roll of a die. The probabilities of rolling an even number, landing on a star space, landing at Cat Town, and not landing on a question mark or star are all different. Thus, only option E applies.
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