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A die is rolled 600 times and the occurr...

A die is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 given below :
`|{:("Outcome"," 1 2 3 4 5 6"),("Frequency"," 200 30 120 100 50 100"):}|` Find the probability of getting a prime number.

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To find the probability of getting a prime number when a die is rolled 600 times, we can follow these steps: ### Step 1: Identify the prime numbers on a die The possible outcomes when rolling a die are 1, 2, 3, 4, 5, and 6. We need to identify which of these numbers are prime: - **1**: Not a prime number (only has one factor). - **2**: Prime number (factors are 1 and 2). - **3**: Prime number (factors are 1 and 3). - **4**: Not a prime number (factors are 1, 2, and 4). - **5**: Prime number (factors are 1 and 5). - **6**: Not a prime number (factors are 1, 2, 3, and 6). **Prime numbers on a die**: 2, 3, and 5. ### Step 2: Find the frequency of the prime outcomes From the given data: - Frequency of 1: 200 - Frequency of 2: 30 - Frequency of 3: 120 - Frequency of 4: 100 - Frequency of 5: 50 - Frequency of 6: 100 The frequencies of the prime numbers are: - Frequency of 2: 30 - Frequency of 3: 120 - Frequency of 5: 50 ### Step 3: Calculate the total frequency of prime outcomes Now, we add the frequencies of the prime numbers: \[ \text{Total frequency of prime outcomes} = \text{Frequency of 2} + \text{Frequency of 3} + \text{Frequency of 5} \] \[ = 30 + 120 + 50 = 200 \] ### Step 4: Calculate the total number of outcomes The total number of outcomes when the die is rolled is given as 600. ### Step 5: Calculate the probability of getting a prime number The probability \(P\) of getting a prime number is given by the formula: \[ P(\text{prime number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Substituting the values we found: \[ P(\text{prime number}) = \frac{200}{600} \] ### Step 6: Simplify the probability To simplify \(\frac{200}{600}\): \[ P(\text{prime number}) = \frac{200 \div 200}{600 \div 200} = \frac{1}{3} \] ### Final Answer The probability of getting a prime number when a die is rolled 600 times is \(\frac{1}{3}\). ---
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