Question

select the correct answer from each drop-down menu. two six-sided fair dice are rolled. the probability that at least one number is odd and the sum of the two numbers is even is . the probability that exactly one number is 6 and the product of the two numbers is at most 15 is .

Answer 1

The probability that at least one number is odd and the sum of the two numbers is even is 1/2. The probability that exactly one number is 6 and the product of the two numbers is at most 15 is 5/18.

Step-by-step explanation:

To find the probability that at least one number is odd and the sum of the two numbers is even, we can break down the possible outcomes. Out of the 36 possible outcomes when two six-sided fair dice are rolled, there are 18 outcomes where at least one number is odd and the sum of the two numbers is even.

Therefore, the probability is:

P(at least one number is odd and the sum is even) = 18/36 = 1/2

To find the probability that exactly one number is 6 and the product of the two numbers is at most 15, we can again break down the possible outcomes. Out of the 36 possible outcomes, there are 10 outcomes where exactly one number is 6 and the product of the two numbers is at most 15.

Therefore, the probability is:

P(exactly one number is 6 and the product is at most 15) = 10/36 = 5/18

Answer 2

Part A: The probability that at least one number is odd and the sum of the two numbers is even is 1/4

Part B: The probability that exactly one number is 6 and the product of the two numbers is at most 15 is 1/9

When the two six-sided fair dice are rolled then we get total of 36 order pairs.

Part A:

In which we have to find the probability that at least one number is odd and the sum of two numbers is even; for this question we get the total of 9 order pairs which are;

(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)

Probability= no. of order pairs that contain at least one number is odd and the sum of two numbers is even) / total no. of order pairs

P= 9/36

P=1/4

Part B:

Four order pairs which will fulfill the condition that exactly one number is 6 and the product of the two numbers is at most 15 are;

(1,6),(2,6),(6,1),(6,2)

Therefore,

Probability= no. of order pairs that exactly one number is 6 and the product of the two numbers is at most 15/ total no. of order pairs

Probability= 4/36

P=1/9