Discuss the following problems:
Q1. Find the probability of a couple having at least 1 girl among 7 children. Assume that boys and girls are equally likely and that the gender of a child is independent of any other child.
Q2. If the couple has seven children and they are all boys, what can the couple conclude?
Q3. Find the probability that a randomly selected subject has a birthday on the 26th of the month, given that the subject is born in June. That is, find P(Birthday on the 26th | June birthday).
Assume we are dealing with a 365 day year.
|
|
Birthday on the 26th
|
Birthday not on the 26th
|
|
Birthday in June
|
1
|
29
|
|
Birthday not in June
|
11
|
324
|
Q4. Find the probability that a randomly selected subject has a birthday in June given that the subject was born on the 26th. That is find P(June birthday | Birthday on the 26th ). Assume we are dealing with a 365 day year.
Q5. The Kentucky Lottery has a Pick 4 lottery game, you pay $1 to select a sequence of four digits, such as 1332. If you select the same sequence of four digits that are drawn, you have a "straight" match and you win $5000.
a) How many different selections are possible?
b) What is the probability of winning?
c) If you win, what is your net profit?
d) Find the expected value.
|
|
x, new profit
|
P(x), Proability
|
x . P(x)
|
|
Win
|
|
|
|
|
Lose
|
|
|
|
|
|
|
E=Σ[ x⋅P?( x)]=
|
|