Probability distributions

Basics

100

A distribution in which the probability of each value for the Random Variable is the same.

Uniform

200

A distribution in which E(X)=np

Binomial

300

A distribution in which E(X)=(ra)/n

Hypergeometric

400

A distribution in which the number of trials is given and the probability remains unchanged for each trial.

Binomial

500

A distribution in which you have a series of dependent trials with only possible outcomes of success and failure for each trial.

Hypergeometric

Uniform Distributions

100

You are offering a fundraiser in which you sell raffle tickets. 2000 tickets are sold in total. If there are 5 grand prize tickets each worth $1 000, and the random variable X represents the prize value, what is P(X=1000)?

1/400

200

A continuous random variable X is uniformly distributed over the interval [10, 16]. The expected value of X is

13

300

You are rolling an 9-sided die numbered 2-10. what is the probability that you roll is between six and ten?

0.55

400

A spinner has 14 equally spaced sections number 1-14. What is the probability the arrow lands on a prime number?

1/2

500

Assume you are rolling a 6-sided die in which each side pays its face value except the side with a 5. What would the $won/lost need to be in order for this to be a fair game?

-16

Binomial Distributions

100

Identify n, p, and q for the following: You roll a pair of standard dice 30 times and note the number of "doubles" that appear

n=30 p=1/6 q=5/6

200

A random sample of 15 people is taken from a population in which 40% favour a particular political stand. What is the probability that exactly 6 individuals in the sample favour this political stand?

0.2066

300

Roll a fair 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is:

0.092

400

If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. If you buy one ticket each month for five months, what is the probability that you will win at least one prize?

0.44

500

There are 10 patients on the Neo-Natal Ward of a local hospital who are monitored by 2 staff members. If the probability (at any one time) of a patient requiring emergency attention by a staff member is .3, assuming the patients to be behave independently, what is the probability at any one time that there will not be sufficient staff to attend all emergencies?

0.6172

Hypergeometric Distributions

100

What is the let statement for the following situation? "A basket contains two types of balls, red and white. If there are 5 red and 45 white balls in the basket. What is the probability that exactly 4 of the 10 are red?"

Let X represent the number of red balls chosen

200

A scientific expedition has captured, tagged, and released eight sea turtles in a particular region. The expedition assumes that the population size in this region is 35, which means that 8 are tagged and 27 not tagged. The expedition will now capture 10 turtles and note how many of them are tagged. If the assumption about the population size is correct, what is the probability that the new sample will have 3 or less tagged turtles in it?

0.85969

300

In Lotto 6-49 you buy a ticket with six numbers chosen from the set {1, 2, . . . , 49}. The draw consists of a random sample drawn without replacement from the same set, and your prize depends on how many “successes” were drawn. What is the probability of you getting 5 numbers right?

1.84 x10 ^-5 or 0.0000184

400

Suppose that there are 5 green and 45 red marbles in an urn. Standing next to the urn, you close your eyes and draw 10 marbles without replacement. What is the probability that exactly 4 of the 10 are green?

0.00396

500

You are drawing cards from a standard deck without replacement. let X = the number of ♠’s in the first 20 draws. What is the probability of drawing exactly 10 spades?

0.00144

COOL STUFF

100

A horse is tied to a 15 ft. rope and there is a bail of hay 25 ft. away from him. Yet the horse is able to eat from the bail of hay. How is this possible?

The rope isn't tied to anything

200

The one who makes it sells it. The one who buys it doesn't use it. The one who's using it doesn't know he's using it. What is it?

coffin

300

What is the value of k? x –3 –2 –1 0 1 2 Pr(X = x) 0.10 k 0.25 0.20 k 0.25

0.1

400

In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: W 0 1 2 3 4 5 P(W) 0.1 0.1 0.25 0.3 0.2 0.05 The probability that a randomly-selected household has at least two cell phones is

0.8

500

The following table gives the probability distribution of the number of people in cars travelling along a certain freeway. p 1 2 3 >3 Pr(P = p) 0.45 0.35 0.05 0.15 A toll of $5.00 is charged on cars which carry only the driver; otherwise the toll per car is only $1.50. The expected toll charge per car is equal to:

$3.08