Question

1. If a person is dealt 5 cards from a standard deck of 52 cards, what is the probability (to four decimal places) of being dealt 4 of a kind?

2. The hypergeometric distribution is a distribution of a variable that has two outcomes when sampling is done without replacement.

Given a population with only two types of objects (females and males, defective and nondefective, successes and failures, etc.), such that there are a items of one kind and b items of another kind and a + b equals the total population, the probability P (X) of selecting without replacement a sample of size n with X items of type a and nX items of type b is

P (X) = aCX  bCnX a+b Cn

A recent study found that four out of nine houses were underinsured. If Öve houses are selected from the nine houses, Önd the probability (to four decimal places) that exactly two are underinsured.

3. A 10 foot by 20 foot rectangular rug is hung outside to dry. Near the center of the rug, is a circle of radius 4 feet. What is probability (to four decimal places) that a fly randomly lands inside the circle?

4. An airplane is built to be able to áy on one engine. If the planeís two engines operate independently, and each has a 1% chance of failing in any given four-hour áight, what is the chance the plane will fail to complete a four-hour áight to Oklahoma due to engine failure?

Answer 1