Finding the Probability of Picking a Family Member's Name: A Case of Two Tries

In summary, the purpose of finding the probability of picking a family member's name is to understand the likelihood of randomly selecting a specific name from a group of names. This is based on the total number of possible outcomes and the number of desired outcomes, and can be calculated by dividing the number of desired outcomes by the total number of outcomes. Conducting two tries can provide a more accurate probability, and the results of this calculation can be interpreted as the likelihood of picking a specific family member's name in a random selection.
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A family of five people randomly picks a name of a family member from a hat to decide for whom to buy a present.
What is the probability that nobody picks their own name?
If someone picks their own name, all the names are returned and everyone picks again. What is the probability that it took exactly two tries for everyone to pick a name of another family member:confused:
 
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The probability of nobody picking their own name on the first try can be calculated by taking the number of ways to choose 5 names out of 4 (since one person cannot pick their own name) and dividing it by the total number of ways to choose 5 names out of 5. This can be expressed as (4/5)*(3/4)*(2/3)*(1/2)= 1/5. Therefore, the probability of nobody picking their own name on the first try is 1/5 or 20%.

If someone does pick their own name, then all the names are returned and everyone picks again. This essentially restarts the process and the probability of nobody picking their own name on the second try would still be 1/5.

The probability of it taking exactly two tries for everyone to pick a name of another family member would be the probability of someone picking their own name on the first try (1/5) multiplied by the probability of nobody picking their own name on the second try (1/5). This can be expressed as (1/5)*(1/5) = 1/25 or 4%.

Overall, the probability of it taking exactly two tries for everyone to pick a name of another family member is 4%.
 

1. What is the purpose of finding the probability of picking a family member's name?

The purpose of finding the probability of picking a family member's name is to understand the likelihood of randomly selecting a specific name from a group of names. This can be useful in various scenarios, such as predicting the chances of picking a family member's name from a hat or determining the probability of a certain family member being chosen for a game or activity.

2. What is the basic concept behind finding the probability of picking a family member's name?

The basic concept behind finding the probability of picking a family member's name is based on the total number of possible outcomes and the number of desired outcomes. In this case, the total number of outcomes is the total number of family members, and the desired outcome is the specific family member's name that is being searched for.

3. How is the probability of picking a family member's name calculated?

The probability of picking a family member's name can be calculated by dividing the number of desired outcomes (i.e. the number of times the specific name appears in the group of names) by the total number of outcomes (i.e. the total number of family members). This can be expressed as a fraction, decimal, or percentage.

4. What is the significance of conducting two tries in this case?

Conducting two tries allows for the calculation of a more accurate probability. In the first try, the probability of picking a family member's name may be influenced by chance. However, in the second try, the chances of picking the same family member's name again are lower, which can provide a more realistic estimation of the probability.

5. How can the results of this probability calculation be interpreted?

The results of this probability calculation can be interpreted as the likelihood of picking a specific family member's name from a group of names. For example, if the probability is 0.25, it can be interpreted as a 25% chance of picking that family member's name in a random selection. It is important to note that this is only a prediction and the actual outcome may differ.

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