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Chapter 35: Problem 1124

If two dice are cast, what is the probability the sum will be less than 5 ?

Short Answer

Expert verified
The probability that the sum of the numbers rolled on both dice will be less than 5 is \(\frac{1}{6}\).

Step by step solution

01

Find the total number of possible outcomes

When two dice are rolled, each die has 6 possible outcomes (1, 2, 3, 4, 5, or 6) and the other die also has 6 possible outcomes. So, the total number of possible outcomes is 6*6 which equals 36.
02

Find the number of outcomes where the sum is less than 5

We need to find the number of possible outcomes where the sum of the numbers rolled on both dice is less than 5. Let's write down the possible outcomes that meet this condition: 1. Die 1 shows 1, Die 2 shows 1 (sum = 2) 2. Die 1 shows 1, Die 2 shows 2 (sum = 3) 3. Die 1 shows 1, Die 2 shows 3 (sum = 4) 4. Die 1 shows 2, Die 2 shows 1 (sum = 3) 5. Die 1 shows 2, Die 2 shows 2 (sum = 4) 6. Die 1 shows 3, Die 2 shows 1 (sum = 4) There are 6 outcomes where the sum is less than 5.
03

Calculate the probability of the sum being less than 5

To find the probability, we will divide the number of outcomes where the sum is less than 5 by the total number of possible outcomes. Probability = (Number of outcomes where the sum is less than 5) / (Total number of possible outcomes) Probability = 6 / 36 Probability = 1 / 6 The probability that the sum of the numbers rolled on both dice will be less than 5 is \(\frac{1}{6}\).

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