PART ONE: Binomial Probabilities

"R" has three functions that we can use to compute binomial probabilities:pbinom, qbinom and dbinom

The functions are written like this:

pbinom(x, n, p),qbinom(x, n, p),dbinom(x, n, p)

Wherex= the number of successes,n= the number of trials andp= the probability of a success on a single trial.

Q1: 10% of a country's population are left-handed.Calculate by hand on theworksheetand also calculate in "R"

a) What is the probability that exactly 5 people in a group of 16 are left-handed?

b) What is the probability that 3 or less people in a group are left-handed?

c) What is the probability that at least 8 people in a group are left-handed?

Q2: An airline has determined that 5% of its customers do not show up for their flights.If a passenger is bumped off a flight because of overbooking, the airline pays the customer $200.There are 200 people booked on a flight.

a) What is the probability that the airline will have to bump exactly 3 passengers?

b) What is the probability that 5 or more passengers will be bumped?

PART TWO: HYPERGEOMETRIC DISTRIBUTION

Q3: A basket of 12 apples has 5 bad apples in it.Four apples are drawn from the basket.

a)Find the probability that 3 will be bad.

b) Find the probability that less than 2 will be bad.

Q4: 5 cards are randomly dealt from a standard deck of cards.

a) Find the probability that 3 are face cards

b) Find theprobability that less than 3 are face cards.

PART THREE: PROBABILITY DISTRIBUTION

Q5: 5 cards are randomly dealt from a standard deck of cards.Find the probability distribution for the number of cards dealt that are face cards.

# of face cards

(x). P(x)

1

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5