Questions: Question 5. A die is rolled. Find the probability of the given event. Round all answers to 4 decimals. (a) The number showing is a 2 ; The probability is : 0 (b) The number showing is an even number; The probability is : 0^8 (c) The number showing is greater than 1 ; The probability is : 0^∞

Question 5. A die is rolled. Find the probability of the given event. Round all answers to 4 decimals. (a) The number showing is a 2 ; The probability is : 0 (b) The number showing is an even number; The probability is : 0^8 (c) The number showing is greater than 1 ; The probability is : 0^∞
Transcript text: Question 5. A die is rolled. Find the probability of the given event. Round all answers to 4 decimals. (a) The number showing is a 2 ; The probability is : $\square$ 0 (b) The number showing is an even number; The probability is : $\square$ $0^{8}$ (c) The number showing is greater than 1 ; The probability is : $\square$ $0^{\infty}$
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Solution

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Solution Steps

To solve these probability questions, we need to understand the basic principles of probability. A standard die has 6 faces, each showing a different number from 1 to 6. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

(a) The probability of rolling a 2 is the number of ways to roll a 2 divided by the total number of outcomes. (b) The probability of rolling an even number is the number of even numbers on the die divided by the total number of outcomes. (c) The probability of rolling a number greater than 1 is the number of outcomes greater than 1 divided by the total number of outcomes.

Step 1: Probability of Rolling a 2

The probability of rolling a 2 can be calculated as follows: \[ P(\text{rolling a 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6} \approx 0.1667 \]

Step 2: Probability of Rolling an Even Number

The even numbers on a die are 2, 4, and 6. Thus, the probability of rolling an even number is: \[ P(\text{rolling an even number}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5000 \]

Step 3: Probability of Rolling a Number Greater than 1

The numbers greater than 1 on a die are 2, 3, 4, 5, and 6. Therefore, the probability of rolling a number greater than 1 is: \[ P(\text{rolling a number greater than 1}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{6} \approx 0.8333 \]

Final Answer

  • The probability of rolling a 2 is \( \boxed{0.1667} \).
  • The probability of rolling an even number is \( \boxed{0.5000} \).
  • The probability of rolling a number greater than 1 is \( \boxed{0.8333} \).
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