Probability

 Suppose you go out for pizza with two friends. You have agreed to the following rule to decide who
will pay the bill. Each person will toss a coin. The person who gets a result that is diGGerent from the other
two will pay the bill. If all three tosses yield the same result, the bill will be shared by all.
B
List the sample space. (Hint: What are the possible combinations of the coin toss?)
C
Find the probability that only you will have to pay.
D
Find the probability that all three will share the expense.
 Suppose “
BOE
#
BSF
UXP
FWFOUT
TVDI
UIBU

P(A)=.50 and P(B)=.22. Answer the following questions.
(a) Determine P(A S B) if A and B are independent.
(b) Determine P(A S B) if A and B are mutually exclusive.
. Let X be a random variable that represents the number of students who are absent on a given day from a
class of 25. The following table lists the probability distribution of X.
x 012345
P(x) .08 .18 .32 .22 .14 .06
(a) Determine the following probabilities. P(X = 4), P(X > 4), P(2 < X  4), and P(X 1).
(b) Determine the expected number of absent students on a given day.
(c) Compute the variance of X by definition.

According to the Mendelian theory of inherited characteristics, a cross fertilization of related spices of red
and yellow flowered plants produces a generation whose oGGTpring contain 25% red-flowered plants. Suppose
that a horticulturist wishes to cross 5 pairs of the cross-fertilized species.
B
Justify that each cross fertilization of the red- and yellow-flowered plants is a Bernoulli trial.
Let X be the number of red-flowered plants in 5 pairs of the cross-fertilized species.
C
Is X a binomial random variable? If Yes, identify n and p.
D
Determine the probability that there will be no red-flowered plant.
E
Determine the probability that there will be at least one red-flowered plant.
F
Determine E(X), V ar(X) and SD(X). (Hint:not necessary to compute through the definition of mean
and variance.)
(d) Determine the standard deviation of X.

Z is a standard normal random variable. Determine the following probabilities.
B
P (0 < Z < 1.96), P (Z < 1.96), and P (Z < 1.96).
C
P (1.5 < Z < 2), and P (1.5 < Z < 2).
D
P (1 < Z < 1), P (2 < Z < 2), and P (3 < Z < 3). Compare these probabilities to those in the
empirical rule.