Test Four - Probability Concepts
0.24
Suppose that A and B are independent events such that P(A)= 0.8 and P(B)= 0.3. Find P(A & B).
The given event is the event that is assumed to have occurred. The given event can restrict the outcomes available to the other event, and the probability that the given event occurs is usually necessary to calculate the conditional probability.
Which event is the "given event"?
0.25
An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs—with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a spade?
0.50
An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs—with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is black?
The two events are not independent because P(B|A) not equal to P(B).
Decide whether or not the two events in question are independent or whether it is not possible to tell. P(B)= 0.7 and P(B|A)= 0.3
0.75
Find the probability of the indicated event if P(E)equals=0.25 and P(F)equals=0.55. Find P(E or F) if P(E and F)equals=0.05
0.92
Find the probability P(E or F) if E and F are mutually exclusive, P(E)equals=0.41, and P(F)equals=0.51
3/13
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a face card is selected is
1
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a face card is selected, given that a king is selected is
3/13
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a face card is selected, given that a club is selected is
1/6
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a face card is selected, given that a king is not selected is
1/13
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a king is selected is
0
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a king is selected, given that a face card is not selected is
1/3
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a king is selected, given that a face card is selected
1/4
A balanced dime is tossed three times. The possible outcomes are represented in the table. HHH HTH THH TTH HHT HTT THT TTT Find the probability that all three tosses come up the same.
1/2
A balanced dime is tossed three times. The possible outcomes are represented in the table. HHH HTH THH TTH HHT HTT THT TTT Find the probability that the secondsecond toss comes up headsheads.
1/8
A balanced dime is tossed three times. The possible outcomes are represented in the table. HHH HTH THH TTH HHT HTT THT TTT Find the probability that nonenone of the tosses comecome up tailstails.
1/4
A balanced dime is tossed three times. The possible outcomes are represented in the table. HHH HTH THH TTH HHT HTT THT TTT Find the probability that the last two tosseslast two tosses come up headsheads.
0.057
A recent census found that 52.5 % of adults are female, 10.6 % are divorced, and 5.7 % are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. Obtain P(F & D).
0.574
A recent census found that 52.5 % of adults are female, 10.6 % are divorced, and 5.7 % are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. Obtain P(F or D).
0.475
A recent census found that 52.5 % of adults are female, 10.6 % are divorced, and 5.7 % are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. Obtain P(male).
0.106
A recent census found that 52.5 % of adults are female, 10.6 % are divorced, and 5.7 % are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. Obtain P(D).
0.525
A recent census found that 52.5 % of adults are female, 10.6 % are divorced, and 5.7 % are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. Obtain P(F).
Event B is said to be independent of event A if P(B|A)=P(B).
What does it mean for event B to be independent of event A?
Three events are mutually exclusive if no two of them have outcomes in common.
What does it mean for three events to be mutually exclusive?
The conditional probability of an event is the probability that one event occurs, under the assumption that another event occurs.
What is conditional probability?
0.5
Suppose that E and F are two events and that Upper P left parenthesis Upper E & Upper F right parenthesisP(E & F)equals=0.1 and Upper P left parenthesis Upper E right parenthesisP(E)equals=0.2. What is Upper P left parenthesis F|E right parenthesisP(F|E)?
Roughly 356 human gestation periods will exceed 9 months.
The probability is 0.356 that the gestation period of a woman will exceed 9 months. In 1000 human gestation periods, roughly how many will exceed 9 months?
1/13
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. The probability that a king is selected, given that a club is selected is
0.75
An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs—with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is not a diamond?
The joint probability equals the product of the marginal probabilities; that is, P(A&B) = P(A) X P(B).
If event A and event B are independent, how can their joint probability be obtained from their marginal probabilities?
0.67
Find the probability P(not E) if P(E)equals=0.33
