Download Discrete Random Variables

Discrete Random Variables
1) You play two games against the same opponent. The probability that you win the first game
is 0.4. If you win the first game, the probability you also win the second is 0.2. If you lose
the first game, the probability that you win the second is 0.3.
a) Are the two games independent? Explain your answer.
b) What is the probability that you lose both games?
c) What is the probability that you win both games?
d) Let random variable X be the number of games you win. Find the probability model
for X. In other words, find the probability of each discrete outcome (winning 0
games, winning one game, winning both games).
X
0
1
2
P(X)
e) What are the expected value and standard deviation of X?
2) In a litter of seven kittens, three are female. You pick two kittens at random, without
replacement.
a) Create a probability model for the number of male kittens you get (make a table like
the one in question 1d).
b) Create a histogram to display the probability model
c) What is the expected number of male cats?
d) What is the standard deviation?
3) Assume that 13% of people are left-handed. Answer the following questions assuming we
pick 5 people at random.
a) Create a probability model for the number of left-handed people, and draw a
histogram to represent it.
b) What is the average number of left-handed people you would expect to find in a
group of 5? What is the standard deviation?
c) Are the events of picking a left-handed person independent? Explain.
d) Find the following probabilities:
i) The first lefty is the 5th person chosen.
ii)
There are some lefties among the five chosen.
iii)
The first lefty is the second or third person.
iv)
There are exactly 3 lefties in the group.
v)
There are at most 3 lefties in the group.
vi)
There are no more than 3 lefties in the group.
e) Which of the situations in d) are binomial? Which are geometric? Which are
neither?
4) If 13% of people are left-handed, then we can assume that 87% are right-handed. Create a
probability model and a histogram for the number of right-handed people in a group of 5
randomly chosen people. How does this distribution compare with that from the question
about left-handed people?