How many children do Person X and Y have?

In summary, X and Y each have four children and there are three movie tickets, with a probability of 6/7 that two tickets will go to the kids of one person and one ticket will go to the kids of the other person. This can be solved using combinatorics, without the use of Baye's theorem, by finding an expression for the probability in terms of the number of children and solving for N. The end result is that both X and Y have four children.
  • #1
Vagrant
195
1
Hi, I'd appreciate help with this problem;

Person X and Y have equal number of kids. There are 3 movie tickets. The probability that 2 tickets go to kids of one and 1 ticket goes to the kids of other is 6/7. How many kids do X and Y have?

Thanx
 
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  • #2
Supposing each way of distributing the tickets is of equal probability, you can find and expression using combinatorics for the desired probability in terms of N (the number of kids). Then set the probability equal to 6/7 and solve for N.
 
  • #3
sorry, but i don't see any connection between the data given and no. of kids, except that both have 2 or more kids. Could u please be more definite.
Thanx for ur help.
 
  • #4
Let X have N children, and Y have N children. For starters, how many ways are there to distribute the 3 tickets among the 2N children?
 
  • #5
Well, i used Baye's theorem n I'm getting the no. of children to be 4, which is correct, thank You for your help.
 
  • #6
shramana said:
Well, i used Baye's theorem n I'm getting the no. of children to be 4, which is correct, thank You for your help.

Baye's theorem is not reqiured:
2(nC2)(nC1)/(2nC3)=6/7 . Solving we get, n=4.
 

Related to How many children do Person X and Y have?

1. What is probability in the context of two groups?

Probability in the context of two groups refers to the likelihood of a certain event occurring within one group compared to another group.

2. How is probability calculated for two groups?

Probability for two groups is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as P = (# of favorable outcomes / total # of possible outcomes).

3. What is the difference between probability and statistics in the context of two groups?

Probability is the measure of the likelihood of an event occurring, while statistics involves analyzing and interpreting data from a sample or population. In the context of two groups, probability is used to determine the likelihood of a certain event occurring within each group, while statistics can be used to compare the characteristics of the two groups.

4. How is probability used in hypothesis testing for two groups?

In hypothesis testing for two groups, probability is used to determine the likelihood of obtaining the observed difference between the two groups if the null hypothesis (no difference between the groups) is true. This is known as the p-value, and a smaller p-value indicates a stronger evidence against the null hypothesis.

5. Can probability be used to make predictions about two groups?

Yes, probability can be used to make predictions about two groups by calculating the probability of a certain event occurring in each group and comparing the probabilities between the two groups. This can help in making informed decisions or identifying patterns and trends within the groups.

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