Assignment
1. You have a biased or unfair coin, such that, on each toss, the probability of observing a
head is .25 and the probability of observing a tail is .75. Let X be the variable: number
of heads observed in 4 tosses.
a) Describe the probability distribution of X and compute the mean and the standard
deviation of this distribution.
2. A multiple-choice test contains 12 questions, 8 of which have 4 answers each to choose
from and 4 of which have 5 answers each to choose from. If a student randomly guesses
all of his answers, what is the probability that he will get exactly 2 of the 4-answer
questions correct and at least 3 of the 5-answer questions incorrect?
3. A standard deck of 52 cards consists of 4 suits (spades, hearts, diamonds, and clubs),
each of which contains 13 cards. A player selects 3 cards at random, without
replacement, and is interested in knowing the mean and standard deviation of X: the
number of diamonds he might select. Compute the answers for him.
4. A store has found that 10% of the items it sells are returned after Christmas. On one
day, a total of 50 items are sold by 5 clerks: Clerk A sold 5 items, Clerk B sold 20
items, and the rest of the items were sold by the other 3 clerks.
a) What is the probability that none of the items sold by Clerk A will be returned?
b) What is the probability that exactly 3 of the items sold by Clerk B will be returned?
c) What is the probability that between 2 and 7 (inclusively) of the items sold by the
other 3 clerks will be returned?
d) What is the probability that between 3 and 6 (inclusively) of the items sold by Clerk
B and that exactly 4 of the items sold by the other 3 clerks will be returned?
5. A bag contains 4 red marbles and 2 blue marbles. You draw a marble at random,
without replacement, until the first blue marble is drawn. Let X = the number of draws.
a) If you repeated this experiment a very large number of times, on average how many
draws would you make before a blue marble was drawn?
b) Express the maximum number of draws you might have to make as a Z score.
c) Suppose you had sampled with replacement. Is it more likely that you would make 1
draw or 6 draws before you got a blue marble? Why?
Answers:
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