Answered

For all your questions, big or small, IDNLearn.com has the answers you need. Get the information you need from our community of experts, who provide detailed and trustworthy answers.

Two dice are rolled together. Using the table provided, find the probability of:

(i) The sum of the digits being more than 6.
(ii) The sum of the digits being less than 3.
(iii) The sum of the digits being either 5 or 6.
(iv) The sum of the digits being 12.
(v) The sum of the digits being more than 5 but less than 9.

Sagot :

GinnyAnsweridn
Let's find the probabilities of various outcomes when two dice are rolled together. When rolling two six-sided dice, there are a total of 6 * 6 = 36 possible outcomes.

Given:
- Total possible outcomes = 36

Let's go through each part of the question in detail:

### (i) Sum of digits to be more than 6
To find the probability that the sum of the digits (numbers on the dice) is more than 6, we look at the number of successful outcomes where this condition is met.

- Number of successful outcomes = 21

The probability is:
[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{21}{36} = 0.5833 \][/tex]

### (ii) Sum of digits to be less than 3
To find the probability that the sum of the digits is less than 3, we consider the relevant outcomes:

- Number of successful outcomes = 1

The probability is:
[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{1}{36} = 0.0278 \][/tex]

### (iii) Sum of digits to be either 5 or 6
To find the probability that the sum of the digits is either 5 or 6, we consider the number of outcomes where this condition is met:

- Number of successful outcomes = 9

The probability is:
[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{9}{36} = 0.25 \][/tex]

### (iv) Sum of digits to be 12
To find the probability that the sum of the digits is exactly 12, we consider the relevant outcomes:

- Number of successful outcomes = 1

The probability is:
[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{1}{36} = 0.0278 \][/tex]

### (v) Sum of digits to be less than 12 but more than 5
To find the probability that the sum of the digits falls in the range between 5 (exclusive) and 12 (exclusive), we count those outcomes:

- Number of successful outcomes = 25

The probability is:
[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{25}{36} = 0.6944 \][/tex]

Thus, summarizing the probabilities:
1. Probability of sum more than 6: [tex]\( 0.5833 \)[/tex]
2. Probability of sum less than 3: [tex]\( 0.0278 \)[/tex]
3. Probability of sum either 5 or 6: [tex]\( 0.25 \)[/tex]
4. Probability of sum equal to 12: [tex]\( 0.0278 \)[/tex]
5. Probability of sum less than 12 but more than 5: [tex]\( 0.6944 \)[/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.