MDM 4UI - Unit 6, Day 5
#1) Identify each distribution as uniform, binomial or hypergeometric
a)
A multiple choice test has 20 questions. Each question has 4
choices with one correct answer and you guess randomly at each
question.
b) You draw 10 cards out of a deck without replacement to determine
the probability of drawing a face card.
c) An experiment consists of flipping a fair coin 8 times and counting
the number of tails.
d) You roll a six-sided die 25 times and count the number of times
each number comes up.
e)
You draw 10 cards out of a deck of cards, replacing the drawn
card after each trial. You are trying to determine the probability of
drawing an ace.
f)
You use a random number generator to produce numbers from 1
to 10. After 50 trials you count how many of each number
appeared.
g)
In a basket of 30 apples, 5 of them are rotten. If you pick 5 apples
out of the basket, what is the probability of getting a rotten one?
h) A factory produces 500 steering wheels in one day but 8 are
known to be defective. If the quality control officer chooses 10
steering wheels at random to test, what is the probability they will
get a defective one?
#2) For each situation below:
a) Determine if it is binomial or hypergeometric
b) Change the scenario so the other distribution could be used.
Scenario 1: To decide who will complete 2 chores, a mother writes the
names of her 5 children on slips of paper and mixes them together in a
bag. Without looking, she picks one name and that sibling is given the
first chore and their name is removed. She then picks a second name
and that sibling is given the second chore. What is the probability that
the two youngest children get the chores?
Scenario 2: 40% of the music on your Spotify account is by Canadian
artists. If you let Spotify pick 10 random songs to play, what is the
probability that 5 of them are by Canadian artists?
#3) A study reports that 5% of adults are afraid to be home alone at
night. If 20 people are randomly selected, calculate the following:
a) The probability that 1 of the selected people is afraid to be home
alone at night.
b) The probability at least 3 of them are afraid to be home alone at
night.
c) The expected number of people who are afraid to be home alone
at night.
#4) There are 15 females in your class of 25 students. The teacher
creates a random group of 5 students. Calculate the following.
1. The probability that 3 or more in the group are not female.
2. The expected number of females in the group.
Independent Practice
Pg. 185 # 1 - 3, 6 - 8