Question

A pet store has seven puppies, including four huskies, two terriers, and one retriever. if rebecka and aaron, in that order, each select one puppy at random, with replacement (they may both select the same one), find the probability of each event in 33 to 36. suppose two puppies are selected as earlier, but this time without replacement (rebecka and aaron cannot both select the same puppy). find the probability of each event in 37 to 42. 1. both select a husky. 2. aaron selects a terrier, given that rebecka sekects a husky. 3. aaron selects a retriever, given that rebecka sekects a husky. 4. aaron selects a retriever, given that rebecka selects a retriever. 5.rebecka selects a retriever. 6. both select a retriever. 7. rebecka selects a retriever.

Option 1: 4/49
Option 2: 2/7
Option 3: 0
Option 4: 1/7

Answer 1

To find the probability of each event, we consider the total number of puppies in the pet store and the number of puppies of each breed. We calculate the probabilities with and without replacement, taking into account the remaining puppies after each selection. The probabilities for each event are as follows: both select a husky (16/49), Aaron selects a terrier given that Rebecka selects a husky (2/3), Aaron selects a retriever given that Rebecka selects a husky (0), Aaron selects a retriever given that Rebecka selects a retriever (1/6), Rebecka selects a retriever (1/7), both select a retriever (1/49), Rebecka selects a retriever (1/7).

Step-by-step explanation:

To find the probability of each event, let's first determine the total number of puppies in the pet store. The pet store has a total of 7 puppies, which include 4 huskies, 2 terriers, and 1 retriever.

With replacement:

1. To find the probability that both Rebecka and Aaron select a husky, we multiply the probabilities. The probability of Rebecka selecting a husky is 4/7 and the probability of Aaron selecting a husky is also 4/7. So the probability is (4/7) * (4/7) = 16/49.
2. To find the probability that Aaron selects a terrier, given that Rebecka selects a husky, we only consider the remaining puppies which are not huskies. There are 7 - 4 = 3 puppies remaining. The probability of Aaron selecting a terrier from these 3 puppies is 2/3. So the probability is 2/3.
3. To find the probability that Aaron selects a retriever, given that Rebecka selects a husky, we consider the remaining puppies which are not huskies. There are 7 - 4 = 3 puppies remaining. Since there is no retriever in the remaining puppies, the probability is 0.
4. To find the probability that Aaron selects a retriever, given that Rebecka selects a retriever, we consider the remaining puppies which are not retrievers. There are 7 - 1 = 6 puppies remaining. The probability of Aaron selecting a retriever from these 6 puppies is 1/6. So the probability is 1/6.
5. To find the probability that Rebecka selects a retriever, we consider the total number of puppies. The probability of selecting a retriever is 1/7. So the probability is 1/7.
6. To find the probability that both Rebecka and Aaron select a retriever, we consider the total number of puppies. The probability of Rebecka selecting a retriever is 1/7 and the probability of Aaron selecting a retriever is also 1/7. So the probability is (1/7) * (1/7) = 1/49.
7. To find the probability that Rebecka selects a retriever, we consider the total number of puppies. The probability of selecting a retriever is 1/7. So the probability is 1/7.

Without replacement:

1. To find the probability that both Rebecka and Aaron select a husky, we consider the remaining puppies after each selection. After Rebecka selects a husky, there are 6 puppies remaining. The probability of Aaron selecting a husky from these 6 puppies is 3/6. So the probability is 3/6.
2. To find the probability that Aaron selects a terrier, given that Rebecka selects a husky, we consider the remaining puppies which are not huskies. After Rebecka selects a husky, there are 3 puppies remaining. The probability of Aaron selecting a terrier from these 3 puppies is 2/3. So the probability is 2/3.
3. To find the probability that Aaron selects a retriever, given that Rebecka selects a husky, we consider the remaining puppies which are not huskies. After Rebecka selects a husky, there are 3 puppies remaining. Since there is no retriever in the remaining puppies, the probability is 0.
4. To find the probability that Aaron selects a retriever, given that Rebecka selects a retriever, we consider the remaining puppies which are not retrievers. After Rebecka selects a retriever, there are 6 puppies remaining. The probability of Aaron selecting a retriever from these 6 puppies is 1/6. So the probability is 1/6.
5. To find the probability that Rebecka selects a retriever, we consider the remaining puppies after each selection. After Rebecka selects a retriever, there are 6 puppies remaining. The probability of selecting a retriever from these 6 puppies is 1/6. So the probability is 1/6.
6. To find the probability that both Rebecka and Aaron select a retriever, we consider the remaining puppies after each selection. After Rebecka selects a retriever, there are 6 puppies remaining. The probability of Aaron selecting a retriever from these 6 puppies is 1/6. So the probability is 1/6.
7. To find the probability that Rebecka selects a retriever, we consider the remaining puppies after each selection. After Rebecka selects a retriever, there are 6 puppies remaining. The probability of selecting a retriever from these 6 puppies is 1/6. So the probability is 1/6.