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Probability
Probability With Combinations
Conditional Probability
Expected Gain
Direct and Inverse Variation
100
What is the probability of drawing a black card out of a standard 52 card deck?
1/2
100
Five cards are dealt from a well-shuffled standard deck. What is the probability of getting all hearts?
.00049
100
2 yellow balls and 3 green balls are placed in a jar. One ball is randomly chosen, its color noted, and the ball is put back into the jar. Find the probability that both balls are the same color.
.01776
100
On a multiple-choice test a student is give 5 possible answers for each question. The student receives 1 point for a correct answer and loses 1/4 point for an incorrect answer If the student has no idea of the correct answer for a particular question and merely guesses, what is the students expected gain or loss on the question?
0
100
The number of calories a person burns and the time spends performing an activity varies directly. A 150lb. person burns 75 cal. by sitting in class 50 min. How long would a person need to sit in class to burn 545 cal.?
363 1/3 minutes
200
Of the 1260 households in a small town, 632 have dogs, 568 have cats, and 114 have both types of pet. If a household is chosen at random, what is the probability that the household has either type of pet?
181/210
200
Five cards are dealt from a well-shuffled standard deck. What is the probability of getting no hearts?
.22
200
In a textbook printing warehouse the books are produced by Machine A or Machine B. Machine A produces 45% of the books and Machine B produces the rest. Of the books produced, 5% of Machine A's are defective and 4% of Machine B's are defective. If a book is defective, what is the probability that is was produced by Machine A?
.506
200
Suppose you are taking a multiple choice test described in the earlier question. Suppose also that on one of the questions you can eliminate 2 of the 5 answers as being wrong. If you guess at one of the remaining 3 answers what is your expected gain or loss on the question?
1/6
200
The speed of water in a whirlpool varies inversely with the radius. If the water speed is 2.5 ft per sec. at a radius of 30ft., what is the speed of the water at a radius of 3ft.?
25ft per sec
300
If a 3-letter "word" is formed by randomly choosing 3 letters from the word OCEAN, what is the probability that it is composed only of vowels?
20
300
13 cards are dealt from a well shuffled standard deck. What is the probability of getting all clubs?
1.57 x 10^-12
300
During the the flu epidemic 35% of the school's students have the flu. Of those with the flu, 90% have high temperatures. However, a high temp. is also possible for people w/o the flu, in fact, the school nurse estimates that 12% of those w/o the flu have high temps. What is the probability that if a student has a temp. that they also have the flu?
.8015
300
A lottery has one $1000 prize, five $100 prizes, and twenty $10 prizes. What is the expected gain from buying one of the 2000 tickets sold for $1 each?
3/20
300
When a seesaw is balanced, each persons weight varies inversely with the distance from the center support. If a person who weighs 90lbs. sits at one end of a 12ft seesaw, how far from the support must a 120lb. person sit in order to balance the seesaw?
4.5ft
400
A number between 100 and 999, inclusive, is chosen at random. What is the probability that it contains no 0's?
81/100
400
A bag contains 5 red marbles and 3 white marbles. If 2 marbles are randomly drawn, one after the other and without replacement, what is the probability that the number of red marbles is 0? 1? 2?
A. .107 B. .536 C. .357
500
ber between 100 and 999, inclusive, is chosen at random. What is the probability that it contains at least one 0?
19/100
500
Free concert tickets are distributed to 4 students chosen at random from 8 juniors and 12 seniors in the school orchestra. What is the probability that free tickets are received by 4 seniors? 3 seniors? 2 seniors? 1 senior? no seniors?
A. .102 B. .363 C. .381 D. .139 E. .014