Question

A) A 40-year-old man in the U.S. has a 0.24% risk of dying during the next year . An insurance company charges $250 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.

Expected Value: $ for the year

B)If you randomly select a letter from the phrase "Ichiro Suzuki is at the top of the lineup," what is the probability that you select a vowel? (Your answer must be in the form of a reduced fraction.)

P(vowel) = ?

C)A jar contains 10 red marbles numbered 1 to 10, 6 blue marbles numbered 1 to 6, and 4 white marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability of the given event. Write your answers as integers or reduced fractions.

-The marble is red.    

-The marble is not red.    

-The marble has the number 3 written on it.    

-The marble is blue with the number 2 written on it.    

-The marble has the number 20 written on it.

Answer 1

A) Profit when the old-man dies = 100000 - 250 = 99750

Loss when the old-man doesn't die = 250

Expected value = 99750 * 0.0024 - 250 * (1 - 0.0024) = -$10

B) Total letters in the phrase = 33

Total vowels in the phrase = 15

P(vowel) = 15/33 = 5/11

C) Total marbles = 10 + 6 + 4 = 20

i) P(red) = 10/20 = 1/2

ii) P(not red) = 1 - P(red) = 1 - 1/2 = 1/2

iii) P(marble has the number 3 written on it) = P(3 of red) + P(3 of blue) + P(3 of white)

                                                                      = 1/20 + 1/20 + 1/20

                                                                      = 3/20

iv) P(marble is blue with the number 2 written on it) = 1/20

v) P(marble has the number 20 written on it) = 0