PROBABILITY
If find:
a) The odds FOR E.
Answer: to
b) The odds AGAINST E.
Answer: to
In an experiment, a ball is drawn from an urn containing 11 orange balls and 7 yellow balls. If the ball is orange, three coins are tossed. Otherwise two coins are tossed.
How many elements of the sample space will have a orange ball ?
How many elements of the sample space are there altogether ?
There are five Oklahoma State Officials: Governor (G), Lieutenant Governer (L), Secretary of State (S), Attorney General (A), and Treasurer (T). Take all possible samples without replacement of size 3 that can be obtained from the population of five officials. (Note, there are 10 possible samples!)
(a) What is the probability that the governor is included in the sample?
(b) What is the probability that the governor, attorney general and the treasurer are included in the sample?
Two six-sided dice are rolled (one red and one green). Some possibilities are (Red=1,Green=5) or (Red=2,Green=2) etc.
(a) How many total possibilities are there?
For the rest of the questions, we will assume that the dice are fair and that all of the possibilities in (a) are equally likely.
(b) What is the probability that the sum on the two dice comes out to be 9?
(c) What is the probability that the sum on the two dice comes out to be 8?
(d) What is the probability that the numbers on the two dice are equal?
5. (Note that an Ace is considered a face card for this problem)
In drawing a single card from a regular deck of 52 cards we have:
(a) P( black or a face card ) =
(b) P( black or a 3 ) =
(c) P( black and a Queen ) =
(d) P( face card or a number card ) =
(e) P( black and a face card ) =
A card is drawn at random from a regular playing card deck of 52 cards. Find the probability that an ace is drawn.
Answer:
Employment data at a large company reveal that 52 % of the
workers are married, that 24 % are college graduates, and
that 1/6 of the college graduates are married.
What is the probability that a randomly chosen worker is:
a) neither married nor a college graduate?
Answer = %
b) married but not a college graduate?
Answer = %
c) married or a college graduate?
Answer = %
A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Royal flush (10, J, Q, K, A all of the same suit).
Answer:
You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.75. With water it will die with probability 0.5. You are 90 % certain the neighbor will remember to water the plant.
When you are on vacation, find the probability that the plant will die.
Answer:
You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?
Answer:
Factories A, B and C produce computers. Factory A produces 3 times as many computers as factory C. And factory B produces 5 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.012, the probability that a computer produced by factory B is defective is 0.021, and the probability that a computer produced by factory C is defective is 0.037.
A computer is selected at random and it is found to be defective. What is the probability it came from factory A?
Answer:
In a survey of 225 people, the following data were obtained relating gender to political orientation:
Republican (R)
Democrat (D)
Independent (I)
Total
Male (M)
83
45
36
164
Female (F)
22
21
18
61
Total
105
66
54
225
A person is randomly selected. What is the probability that the person is:
a) Male?
b) Male and a Democrat?
c) Male given that the person is a Democrat?
d) Republican given that the person is Male?
e) Female given that the person is an Independent?
f) Are the events Male and Democrat independent? Enter yes or no .
On average 68 % of Finite Mathematics students spend some time in the Mathematics Department's resource room. Half of these students spend more than 90 minutes per week in the resource room. At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table:
Time spent in resource room
Pass %
None
27
Between 1 and 90 minutes
52
More than 90 minutes
69
If a randomly chosen student did not pass the course, what is the probability that he or she did not study in the resource room?
Answer:
Of 340 male and 260 female employees at the Flagstaff Mall, 220 of the men and 180 of the women are on flex-time (flexible working hours). Given that an employee selected at random from this group is on flex-time, what is the probability that the employee is a woman?
Answer:
Events , and form a partiton of the sample space S with probabilities
, , .
If E is an event in S with , , , compute