PSYCH 104 - CH5 Probability Test

For two mutually exclusive outcomes, one or the other outcome can occur (A or B) but not both (A and B).

p( A ⋃ B) = p( A) + p( B), where ⋃ is the symbol for "or." (additive rule) p( A ⋂ B) = 0, where ⋂ is the symbol for "and."

A bag has 10 blue chips, 10 red chips, 10 green chips, and 10 white chips. The probability of blindly picking a red and green chip in one try will be

p(10chips)=10/40=.25 p(chips Red ⋂ Green)=.25x.25= .06

Two outcomes are ____________ when the sum of their probabilities is equal to 1.00.

complementary

Two outcomes are ________ when the probability of one outcome is dependent on the occurrence of the other outcome.

conditional

An outcome is dependent when

the probability of its occurrence is changed by the occurrence of the other outcome.

The expected outcome is the sum of the products for each random outcome multiplied by the probability of its occurrence.

true

A poll showed that students had no preference among four times during which a class was offered. In this case, the probability of any specific time would be

1/4

The closer to_____, the more probable an event is; the closer to____, the less probable an event is.

1;0

The probability that two independent outcomes occur is equal to the product of their individual probabilities.

p( A ⋂ B) = p( A) × p( B) - Multiplicative rule

The probability of an outcome is the same as the relative frequency of its occurrence.

true

The SD of a binomial distribution is the square root of the variance.

true

Two outcomes are mutually exclusive when

two outcomes cannot occur together

The multiplicative rule is used for conditional outcomes.

false

Four relationship between the outcomes

mutually exclusive; independent; complementary; conditional

The probability of an outcome or event is

the fraction of times an outcome is likely to occur.

State whether each of the following is an appropriate probability. a) p = .88 b) p = −. 26 c) p = 1.45 d) p = 1.00

a) Yes; b) No, cannot be negative; c) No, cannot be greater than 1; d) Yes

Two outcomes (A and B) are mutually exclusive, where p( A) = .45 and p( B) is .28. 1. What is the probability of A and B? 2. What is the probability of A or B?

1. p=0; 2. p=.45+.28=.73

____________ is the proportion or fraction of times an outcome is likely to occur.

Probability

Which of the following is a characteristic of probability?

Probability varies between 0 and 1.

What rule states that when two outcomes for a given event are mutually exclusive, the probability that any one of these outcomes occurs is equal to the sum of their individual probabilities?

The additive rule

A binomial probability distribution is constructed for fixed variables that have at least two possible outcomes.

false

Outcomes in a random event ____, whereas outcomes in a fixed event are _____.

can vary; always the same

Two outcomes are ____________ when the probability of one outcome does not affect the probability of the second outcome.

independent

Bayes's theorem (law)

is a mathematical formula that relates the conditional and marginal (unconditional) probabilities of two conditional outcomes that occur at random. p(A/B)=p(B⋂A)/p(B)

The additive rule is used to define mutually exclusive outcomes.

true

The additive rule states

that when two outcomes for a given event are mutually exclusive, the probability that any one of these outcomes occurs is equal to the sum of their individual probabilities.

Two outcomes are conditional (or dependent) when

the occurrence of one outcome changes the probability that the other outcome will occur.

When two outcomes are independent

the probability of one outcome does not affect the probability of the second outcome.

When two outcomes are complementary,

the sum of their probabilities is equal to 1.00. p( A) + p( B) = 1.00 p( A) = 1 − p( B) p( B) = 1 − p( A)

When two outcomes are complementary, subtracting 1 from the probability of one outcome

will give you the probability for the second outcome.

State whether each of the following two events are complementary. 1. Winning and losing (assuming no ties) a game 2. Studying and playing a video game on the day of an exam 3. Donating money and not donating money to a charity

1. complementary; 2. Not complementary; 3. complementary

A researcher has participants complete a computer task where they can choose to play one of 200 games. Of the 200 games, only 80 are set up so that participants can win the game. 1. What is the event in this example? 2. What is the outcome, x, in this example? 3. What is the probability that a participant will choose a game that he or she can win?

1. selecting ONE game; 2. Selecting a game that a participant can win; 3. p(x)=f(x)/sample space =80/200=.40

A researcher determines that the probability of winning of a new outcome in his experiment is p = .45. Assuming that a new and old outcome are mutually exclusive events, the probability of an old or new outcome would be

1.00

If there are four Aces in a deck of 52 cards, then what is the probability of selecting one Ace on a single draw from the deck of cards?

4/52

The following are six random outcomes for a sample space: −.25, −.5, −.5, −.5, −.5, and −.6. What is the probability of selecting a −.5 in this example?

4/6

What rule states that the product of the individual probabilities for two independent outcomes is equal to the probability that both outcomes occur?

The multiplicative rule.

For a conditional probability we are asking about the probability of one outcome,

given that another outcome occurred.

Conditional probabilities are stated as the probability of

one event (A), given that another event (B) occurred.

The probability of Sam studying (S) for an exam is p = .35. The probability of Sam studying for the exam and earning an A on the exam is p = .20. Hence, the probability of Sam earning an A on the exam, given that he has studied is

p(A/S)= .20/.35= .57

Two outcomes (A and B) are independent, where p( A) = .45 and p( B) is .28. What is the probability of A and B?

p(A⋂B)=.45×.28=.13

The probability that a participant is married is p(M) = .60. The probability that a participant is married and "in love" is p( M ⋂ L) = .46. Assuming that these are random events, what is the probability that a participant is in love, given that the participant is married?

p(L/M)= p(M⋂L)/p(M)= .46/.60= .77

A researcher records the number of interviews a person has to attend before landing a successful job. She finds that the probability of landing a job after one interview is p = .14; two interviews is p = .36; three interviews is p = .32; and four interviews is p = .10. What is the probability that a person lands a job after at least two interviews?

p(least 2interviews)= .14+.36= .50