Deck 14: Probability

Question 1

What is the formula for the joint occurrence of two dependent events?

A)P(a and b) = P(a) × P(b if a)
B)P(a and b) = P(a) + P(b if a)
C)P(a or b) = P(a) × P(b if a)
D)P(a or b) = P(a) + P(b if a)

Answer 1

P(a and b) = P(a) × P(b if a)

Question 2

Which of the following is an example of the joint occurrence of two independent events?

A)drawing the king of clubs from a deck of cards in two draws replacing the first card after the first draw
B)drawing the king of clubs from a deck of cards in two draws not replacing the first card after the first draw
C)drawing an ace or a deuce from a deck of cards in two draws not replacing the first card after the first draw
D)None of the above

Answer 2

drawing the king of clubs from a deck of cards in two draws replacing the first card after the first draw

Question 3

My insurance agent claims that my chances of living to age sixty-five (as a non- smoking female) are 75%.However, another agent, from another agency, told me just last week that my chances are better than 78%.What is the most reasonable explanation for these different figures?

A)One agent is giving me false numbers to justify charging a higher rate for life insurance.Both sets of numbers cannot be accurate at the same time.
B)One agent is using more accurate figures than the other.One set is obviously incorrect.
C)They are both correct-both are judging probabilities based on the evidence available.
D)Statistics cannot really tell us anything reliable about what has not happened.

Answer 3

They are both correct-both are judging probabilities based on the evidence available.

Question 4

What is the probability of rolling at least one three on a single roll of three dice?

A)1/6 × 1/6 × 1/6 = 1/216
B)1/6 × 1/6 × 1/6 = 1/18
C)1/6 +1/6 + 1/6 = 1/2
D)1/2 + 2/6 + 3/6 = 5/6

Question 5

I have two cars.I need to know the probability of at least one of my cars starting in the morning.To figure this out, I take the probability that each car itself will start, and:

A)I add them together.
B)I multiply them together.
C)I add them together and subtract from one.
D)I add them together and subtract the possibility of their joint occurrence.

Question 6

I would like to know my chances of surviving to see my son's high-school graduation.I need to live another twelve years, of course, and my son has to live that long as well-and he also has to graduate! What formula would I use to calculate my chances?

A)the addition theorem for mutually exclusive alternatives
B)the addition theorem for nonexclusive alternatives
C)the general product theorem for the joint occurrence of independent events
D)the general product theorem for the joint occurrence of dependent events

Question 7

I have two jars of coins.One jar contains fifteen coins (five pennies and ten dimes) and the other contains twenty coins (ten of each).What are my chances of drawing two of the same coin if I take one coin from each jar?

A)1/2 + 15/20 = 125%
B)1/6 × 1/3 = 5.5%
C)1/2 × 15/20 = 37.5%
D)1/6 + 1/3 = 50%

Question 8

Where investments are concerned, safety and productivity are considerations that always:

A)serve as indicators of each other
B)complement each other
C)get in the way of a rational assessment of an investment
D)pull in opposite directions

Question 9

I have $400 to invest.I am considering buying a CD (which will pay 6%), but I also just got a prospectus from a corporation selling bonds, which promises 24%.I don't
know where to put my money! That is probably because:

A)I don't know what the expectation value of the CD is.
B)I don't know what the expectation value of the bond is.
C)I don't know the probability of the corporation making good on the bond.
D)I don't know what the return on the bond is.

Question 10

I take the separate probabilities of at least one of two events (which cannot both happen at once) and add them together.I am trying to figure:

A)a joint occurrence
B)an alternate occurrence of mutually exclusive events
C)an alternate occurrence of nonexclusive events
D)the expectation value of the occurrences

Question 11

Two events are mutually exclusive when the occurrence of one prevents the occur-
rence of the other thereafter.

Question 12

To figure the probability of either of two mutually exclusive events (A or B) occurring, the probability of B occurring is subtracted from the probability of A occurring.

Question 13

We use the addition theorem to compute the probability of the alternative occur-
rences of nonexclusive events.

Question 14

To figure the probability of getting at least one head on your first two coin tosses,
figure out how likely it would be not to get any heads at all, and subtract from one.

Question 15

"Expectation value" is the calculated value of a wager or investment, taking into
account not only the value but also the probability of each possible return.

Question 16

Matching:

-The two formulas for the calculation of the probability of the joint occurrence of simple events are known as the ________ theorem.

A)product
B)addition
C)independent

Question 17

Matching:

-The probability of a complex event that consists of nonexclusive alternatives can be computed by changing it into a set of mutually exclusive alternatives, and then
using the ________ theorem

A)addition
B)product
C)expectation value

Question 18

Matching:

-In the __________ view of probability, we figure the probability of the occurrence of an event by dividing the number of ways in which the event can occur by the total
number of equipossible outcomes.

A)a priori
B)relative frequency
C)product

Question 19

Matching:

-Events are called ________ if the occurrence or nonoccurrence of one has no effect upon the occurrence or nonoccurrence of the other.

A)probable
B)independent
C)dependent

Question 20

Matching:

-To compute the probability of the joint occurrence of two independent events, you ________ their separate probabilities together.

A)add
B)subtract
C)Multiply