4.4 Hypergeometric Distributions
Chapter
Chapter 4
Section
4.4
Solutions 16 Videos

A bag contains five red and six blue blocks. What is the probability of getting three red blocks if four blocks are randomly selected? 0.32mins
Q1

Which is an example of a hypergeometric distribution?

A probability of the number of aces in a seven-card hand

B probability of each sum when two dice are rolled

C probability of a number being randomly chosen from the numbers 1 to 10

D probability of the number of times a 3 occurs when rolling a die six times

1.39mins
Q2

Each expression represents the probability of a hypergeometric probability. State the values of the unknowns. 0.56mins
Q3

Show the hypergeometric probability distribution for an experiment with

n = 15, r= 4, a= 7

2.06mins
Q4a

Show the hypergeometric probability distribution for an experiment with

n =8, r= 4, a= 4

1.22mins
Q4b

A five-card hand is dealt from the honour cards in a standard deck (10, J, Q, K, A).

a) Show the probability distribution for the number of hearts in the hand.

b) Calculate the expectation in two ways.

3.11mins
Q5

In a box of 20 light bulbs, five are defective. Three light bulbs are selected at random.

a) What is the probability that at least one is defective?

b) What is the expected number of defective light bulbs?

c) What is the meaning of P(3) in this context?

2.25mins
Q6

In the card game of bridge, 13 cards are dealt to each player. Find the probability of each of the following hands:

a) 4aces

b) at least 1 king

c) 5 clubs, 8 diamonds

1.45mins
Q7

A laboratory has 30 mice, eight of which have a specific genetic mutation. A lab assistant randomly selects 10 of the mice. Which has a greater probability of the mice having the genetic mutation, fewer than three, or more than seven? Explain.

2.26mins
Q8

In a provincial park, 200 foxes are tagged. In 100 sightings, 14 were tagged. Estimate the size of the fox population.

1.18mins
Q9

Wildlife officials tagged 80 deer in an area that had approximately 120 deer.

If they later took a sample of 25 deer, how many would they expect to have been tagged?

1.14mins
Q10a

a) Which will have a greater probability, a seven-card hand with no spades, or a five—card hand with no spades.

b) Verify mathematically and explain any discrepancies with your prediction.

1.07mins
Q11

The members of an antique car club own one car from the 19203, two cars from the 19303, four cars from the 19405, SIX. cars from the 19508, and seven cars from the 19605. They have been invited to send four cars to a car show and will choose them at random.

a) Compare the probabilities of sending all four cars from any given decade.

b) Show the probability distribution for the number of cars selected from the 19505 or 19605, in table form and graphically.

c) What is the expected number of cars sent from the 19405?

d) How would the graph of the distribution in part b) change if there were an additional three cars from the 19203?

5.27mins
Q12

A jury of 12 people is to chosen from a pool of 9 men and 11 women.

Graph the probability distribution for the number of men on the jury.