Question

Two 4 sided dice are thrown. If X=the sum of the scores on the
two dice, what is P(3 ≤ X ≤ 5)?

Answer 1

To find the probability of the sum of two 4-sided dice being between 3 and 5, we list all outcomes and count the favorable ones. There are 9 ways to achieve this out of 16 possible outcomes, making the probability 9/16.

Step-by-step explanation:

The question asks about finding the probability of the sum of the numbers on two rolled 4-sided dice ranging between 3 and 5 inclusive. To find P(3 ≤ X ≤ 5), we list all the possible outcomes (the sample space) for the throw of two 4-sided dice.

Let's denote the two dice as Die 1 and Die 2:

• Die 1 can land on any number from 1 to 4.
• Die 2 can also land on any number from 1 to 4.

Now, we calculate the probability:

1. The possible sums that are between 3 and 5 are: 3, 4, and 5.
2. We count the number of ways to obtain each of these sums:

• For sum 3: (1,2), (2,1) - 2 ways.
• For sum 4: (1,3), (2,2), (3,1) - 3 ways.
• For sum 5: (1,4), (2,3), (3,2), (4,1) - 4 ways.

There are 4 x 4 = 16 total possible outcomes when rolling two 4-sided dice.The number of favorable outcomes for the event 3 ≤ X ≤ 5 is 2 + 3 + 4 = 9.Thus, the probability P(3 ≤ X ≤ 5) is 9/16.

This probability can be mathematically stated as: P(3 ≤ X ≤ 5) = 9/16.