For each problem you need to submit the following: A worksheet for the values (.
ID: 3245899 • Letter: F
Question
For each problem you need to submit the following:
A worksheet for the values (.xls or .xlsx file);
A worksheet for the formulae (.xls or .xlsx file);
Simulation report (.xls or .xlsx file);
a) Say you know a family has two children, and further that at least one of them is a girl. What is the probability that they have two girls?
b) Say you know a family has two children, and further that at least one of them is a girl born on Monday. What is the probability that they have two girls?
Should the answer be the same as in (a)?
Verify your answers using YASAI. You can make the following assumptions: - probability for a girl to be born on Monday: 1/7,
- total number of families with two children: 5,000,000.
Explanation / Answer
Answer to part a)
if there are 2 children
there are 4 possibilites
bb
bg
gb
gg
(where b means boy and g means girl)
.
If atleast one is girl: then there are 3 such cases
we need to find the probability that both are girls, there is only 1 such case
P(2girls given atleast 1 is girl) = 1/3
.
Answer to part b)
P(atleast 1 girl) = 1/7 * 3/4
P(both girls with one girl born on monday) = 1/4 * 1*7
P(both girls with one girl born on monday | at least 1 girl with one born on monday) = (1/4 * 1/7 ) / (3/4 * 1/7)
P(both girls with one girl born on monday | at least 1 girl with one born on monday) = 1/3
.
[Thus we find that probability is same for part a and b]
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