- math: statistic/ probalitity - need help with problem#2-77(a&b, a-c) - please

Question

- math: statistic/ probalitity
- need help with problem#2-77(a&b, a-c)
- please explain the correct answer to each questions
- all information is there in picture
- thank you

2-77. Janelle's aunt and uncle had three children. Two of them were girls. Since girls and be boys are equally likely, Janelle thought that the chance of having two or more must be 50%. Janelle's brother thought the chance of having so many girls had to less than 50%. girls What do you think? Make a conjecture about the probability of having two or three girls in a family of three siblings. a. b. Do a computer simulation to estimate the probability of having two or three girls in a family of three siblings. Your teacher will show you how to simulate a family of three siblings

Explanation / Answer

2.77 a)

Instances of 0 girl :- BBB

Instances of 1 girl :- BBG, GBB, BGB

Instances of 2 girls :- BGG,GBG, GGB

Instances of 3 girls :- GGG

Hence the probability of 2 or more girls out of 3 children will be 4/8 = 0.5 .

2.77 b)

Computer simulation steps:-

- Generate a random number (0-1)

- If number is less than 0.5 it is a girl, if it is more than 0.5 it is a boy

Generate 3 instances of random numbers per trial and map them to girl or booy.

- Execute this step large number of times ( say 10000). Identify the number of trials where number of girls >=2.

- Calculate the probability from this data

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a) Probability of both dice being even is 1/4 = 0.25

b) Simulation will have the following steps:-

- Initialize hit count to 0.

- Generate a random number (1-6) , lets call it A

- Generate another random number (1-6) , lets call it B

- Identify if both A and B are even. If so increment the hit count by 1.

- Execute the above steps large number of times ( say 10000). Compute the hitcount.

- Calculate the probability from this data

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