Answer :
Sure, let's solve this problem step-by-step.
1. Identify the favorable outcomes:
When rolling a number cube (die), there are 6 faces with numbers 1 through 6. We are interested in rolling a number less than 3. The numbers less than 3 on a die are 1 and 2.
2. Determine the number of favorable outcomes:
There are 2 numbers (1 and 2) that satisfy our condition. Hence, the number of favorable outcomes is 2.
3. Determine the total possible outcomes:
Since there are 6 faces on the die, each with an equally likely outcome, the total possible outcomes are 6.
4. Calculate the probability of rolling a number less than 3:
The probability ([tex]\(P\)[/tex]) of rolling a number less than 3 is the number of favorable outcomes divided by the total possible outcomes.
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{2}{6} = \frac{1}{3} \][/tex]
5. Convert the probability to decimal form:
[tex]\[ P = \frac{1}{3} \approx 0.3333333333333333 \][/tex]
6. Determine the number of trials:
The problem states that the die is rolled 24 times. So, the number of trials is 24.
7. Calculate the expected number of times a number less than 3 will be rolled:
The expected value ([tex]\(E\)[/tex]) can be found by multiplying the probability by the number of trials.
[tex]\[ E = P \times \text{Number of Trials} = 0.3333333333333333 \times 24 = 8.0 \][/tex]
Therefore, the expected number of times a number less than 3 will be rolled in 24 trials is 8.0.
1. Identify the favorable outcomes:
When rolling a number cube (die), there are 6 faces with numbers 1 through 6. We are interested in rolling a number less than 3. The numbers less than 3 on a die are 1 and 2.
2. Determine the number of favorable outcomes:
There are 2 numbers (1 and 2) that satisfy our condition. Hence, the number of favorable outcomes is 2.
3. Determine the total possible outcomes:
Since there are 6 faces on the die, each with an equally likely outcome, the total possible outcomes are 6.
4. Calculate the probability of rolling a number less than 3:
The probability ([tex]\(P\)[/tex]) of rolling a number less than 3 is the number of favorable outcomes divided by the total possible outcomes.
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{2}{6} = \frac{1}{3} \][/tex]
5. Convert the probability to decimal form:
[tex]\[ P = \frac{1}{3} \approx 0.3333333333333333 \][/tex]
6. Determine the number of trials:
The problem states that the die is rolled 24 times. So, the number of trials is 24.
7. Calculate the expected number of times a number less than 3 will be rolled:
The expected value ([tex]\(E\)[/tex]) can be found by multiplying the probability by the number of trials.
[tex]\[ E = P \times \text{Number of Trials} = 0.3333333333333333 \times 24 = 8.0 \][/tex]
Therefore, the expected number of times a number less than 3 will be rolled in 24 trials is 8.0.
