Question

Question 4: A-E parts

A) Consider rolling two four sided dice. One die is blue and the other is green.

(1) State the sample space.

(2) Compute the probability of getting two even numbers.

(3) Compute the probability of getting an even sum if the blue die rolls a 2.

B)

(1)What is the probability of drawing a four or a heart when drawing a single card from a standard deck of cards?

C) Consider a machine that fills 275 gallon tanks of water. The owner discovers that the machine does not always dispense exactly 275 gallons. Instead, they discover that it fills between 272 and 275 gallons. 25% of the time it will fill between 272 and 273 gallons of water, 20% of the time it fills between 273 and 274 gallons, and 55% of the time it fills between 274 and 275 gallons.

(1) What is the random variable? Is this discrete or continuous?

(2) If the variable is discrete, state the sample space. If the variable is continuous, give the density curve.

(3) What is the probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water?

D) The lowest dose of an antibiotic works 89% of the time. 5% of the time, a stronger dose is needed.In the remaining case, the bacteria is said to be resistant to the antibiotic. Suppose three patients are given the antibiotic.

(1) What is the probability that at least two patients will need a stronger dose?

(2) What is the probability that the bacteria is resistant in all three patients?

E) Mammography is used as a form of early detection of breast cancer in women. We know that if a woman has breast cancer, mammography will detect it 90% of the time. If the woman does not have breast cancer, then mammography will give a positive result 7% of the time. We also know that there is a 0.8% chance that any given woman has breast cancer.

(1) What is the probability that a woman has breast cancer if she has a positive mammogram?

Answer 1

There are 4 cards out of 52 which are four.

13 cards which are heart.

1 card of heart which four.