To determine which pairs of events are mutually exclusive, we need to understand what mutually exclusive events are. Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other cannot.

I. E and F: Event E is getting two prime numbers. The prime numbers on a die are 2, 3, and 5. Event F is getting a sum that is a prime number. The possible sums of two prime numbers on a die are 4, 5, 6, 7, 8, and 10. Among these, 5, 7 are prime numbers. So, events E and F can occur at the same time. Therefore, E and F are not mutually exclusive.

II. E and G: Event E is getting two prime numbers. Event G is getting a product that is a prime number. The only way to get a prime product with a die is to roll a 2 and a prime number (2, 3, or 5). However, rolling two prime numbers could also result in a product of 4, 6, 9, 10, 15, or 25, which are not prime. So, events E and G can occur at the same time. Therefore, E and G are not mutually exclusive.

III. F and G: Event F is getting a sum that is a prime number. Event G is getting a product that is a prime number. The only way to get a prime product is to roll a 2 and a prime number (2, 3, or 5). However, the sums of these rolls are 4, 5, and 7. Among these, only 5 and 7 are prime. So, events F and G can occur at the same time. Therefore, F and G are not mutually exclusive.

So, none of the pairs of events E and F, E and G, F and G are mutually exclusive.

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To determine which pairs of events are mutually exclusive, we need to understand what mutually exclusive events are. Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other cannot.

I. E and F: Event E is getting two prime numbers. The prime numbers on a die are 2, 3, and 5. Event F is getting a sum that is a prime number. The possible sums of two prime numbers on a die are 4, 5, 6, 7, 8, and 10. Among these, 5, 7 are prime numbers. So, events E and F can occur at the same time. Therefore, E and F are not mutually exclusive.

II. E and G: Event E is getting two prime numbers. Event G is getting a product that is a prime number. The only way to get a prime product with a die is to roll a 2 and a prime number (2, 3, or 5). However, rolling two prime numbers could also result in a product of 4, 6, 9, 10, 15, or 25, which are not prime. So, events E and G can occur at the same time. Therefore, E and G are not mutually exclusive.

III. F and G: Event F is getting a sum that is a prime number. Event G is getting a product that is a prime number. The only way to get a prime product is to roll a 2 and a prime number (2, 3, or 5). However, the sums of these rolls are 4, 5, and 7. Among these, only 5 and 7 are prime. So, events F and G can occur at the same time. Therefore, F and G are not mutually exclusive.

So, none of the pairs of events E and F, E and G, F and G are mutually exclusive.

Knowee AI · Accepted Answer

To determine which pairs of events are mutually exclusive, we need to understand what mutually exclusive events are. Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other cannot.

I. E and F: Event E is getting two prime numbers. The prime numbers on a die are 2, 3, and 5. Event F is getting a sum that is a prime number. The possible sums of two prime numbers on a die are 4, 5, 6, 7, 8, and 10. Among these, 5, 7 are prime numbers. So, events E and F can occur at the same time. Therefore, E and F are not mutually exclusive.

II. E and G: Event E is getting two prime numbers. Event G is getting a product that is a prime number. The only way to get a prime product with a die is to roll a 2 and a prime number (2, 3, or 5). However, rolling two prime numbers could also result in a product of 4, 6, 9, 10, 15, or 25, which are not prime. So, events E and G can occur at the same time. Therefore, E and G are not mutually exclusive.

III. F and G: Event F is getting a sum that is a prime number. Event G is getting a product that is a prime number. The only way to get a prime product is to roll a 2 and a prime number (2, 3, or 5). However, the sums of these rolls are 4, 5, and 7. Among these, only 5 and 7 are prime. So, events F and G can occur at the same time. Therefore, F and G are not mutually exclusive.

So, none of the pairs of events E and F, E and G, F and G are mutually exclusive.

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