If two fair dice are tossed together. What is the probability that the score will be
A) A prime number
B)A perfect square
C) perfect square
D)A total of 4
The bot missed 3 of the 4 questions.
Create a matrix and just count the entries that apply
A) I counted 18 entries that were prime
prob(prime) = 18/36 = 1/2
B) Possible perfect squares are : 4, and 9
I counted 9 of those
prob(perfect square) = 9/36 = 1/4
C) this is the same as B
D) I see only 5 4's, so
prob(a 4) = 5/36
oops, I miscounted
A)prob(prime) = 15/36 = 5/12
B) only 7 perfect squares, so prob(perfect square) = 7/36
C) ....
D) prob(sum of 4) = 3/36 1/12
To find the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.
For this question, we'll look at each letter separately:
A) A prime number:
Prime numbers are 2, 3, 5, and 7 from 1 to 6. Out of the 36 possible outcomes when two dice are rolled, the favorable outcomes are (2, 3), (3, 2), (2, 5), (5, 2), (3, 5), (5, 3). Hence, the probability of rolling a prime number is 6/36, which simplifies to 1/6.
B) A perfect square:
Perfect squares are 4 and 9 from 1 to 6. The favorable outcomes are (2, 2) and (3, 3) out of the 36 possible outcomes. Therefore, the probability of rolling a perfect square is 2/36, simplifying to 1/18.
C) Perfect square:
In this case, we consider both perfect squares from the previous letter, 4 and 9. The favorable outcomes are (2, 2) and (3, 3) out of 36 possible outcomes. So, the probability of rolling any perfect square is also 2/36 or 1/18.
D) A total of 4:
To find the favorable outcomes for a total of 4, we need to find all the possible combinations of numbers rolled that sum up to 4: (1, 3), (3, 1), and (2, 2). These are three favorable outcomes out of the 36 possible outcomes. Thus, the probability of rolling a total of 4 is 3/36, reducing to 1/12.
By calculating the probabilities for each letter, we can determine the likelihood of each scenario occurring when two fair dice are rolled together.
A) 1/9
B) 1/9
C) 1/4
D) 1/36