A bag contains five red and six blue blocks. What is the probability of getting three red blocks if four blocks are randomly selected?
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
Each expression represents the probability of a hypergeometric probability. State the values of the unknowns.
Show the hypergeometric probability distribution for an experiment with
n = 15, r= 4, a= 7
Show the hypergeometric probability distribution for an experiment with
n =8, r= 4, a= 4
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.
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?
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
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.
In a provincial park, 200 foxes are tagged. In 100 sightings, 14 were tagged. Estimate the size of the fox population.
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?
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.
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?
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.
Calculate the probability that a bridge hand of 13 cards contains four cards of one suit and three of each other suit.
A bag contains three nickels, five dimes, and four quarters. Three coins are removed at random. What is the probability that the value of the coins will total 75 cents?