Download PROBABILITY EXAM 1 (1) A red die has the numbers 1, 3, and 5

PROBABILITY EXAM 1
(1) A red die has the numbers 1, 3, and 5 printed on its faces with each number appearing twice. A green die has
the numbers 2, 4, and 6 on its faces with each number appearing twice. You roll the two dice. What is the
probability that the sum of the two numbers rolled is equal to 7?
(a) 1/6
(b) 1/4
(c) 1/5
(d) 1/3
(e) 2/3
(2) You flip three fair coins. What is the probability that you obtain at least one Head and at least one Tail?
(a) 2/8
(b) 3/8
(c) 4/8
(d) 5/8
(e) 6/8
(3) You select a point at random from the unit square. What is the probability that at least one of the coordinates
of the point lies between 1/3 and 2/3?
(a) 2/9
(b) 3/9
(c) 4/9
(d) 5/9
(e) 6/9
(4) You have seven kittens. Four are white and three are black. You cannot distinguish one white kitten from
another and you cannot distinguish one black kitten from another. In how many distinguishable ways can you
line up the kittens for a picture?
(a) 25
(b) 35
(c) 45
(d) 55
(e) 65
(5) You select two points independently from the interval [0, 1]. What is the probability that the distance between
the points is less than 1/4? (Hint translate the problem into one involving the unit square.)
(a) 6/16
(b) 7/16
(c) 8/16
(d) 9/16
(e) 10/16
(6) Select a number X at random from the unit interval with the uniform distribution. What is the probability
that Xis greater than 1/2 given that X is less than 3/4?
(a) 1/3
(b) 1/4
(c) 1/2
(d) 2/3
(e) 3/4
(7) An urn contains 5 red and 5 blue balls. You withdraw balls from the urn one at a time until you draw a red
ball. You do not replace the balls after you withdraw them. What is the probability that it takes at least three
draws to get a red ball?
(a) 2/9
(b) 3/9
(c) 4/9
(d) 5/9
(e) 7/9
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(8) Suppose X is a random variable with density function
√
k x
if
0≤x≤1
f (x) =
0
otherwise
where k is a constant. What is the probability that X is less than 1/4?
(a) 1/16
(b) 2/16
(c) 3/16
(d) 4/16
(e) 5/16
(9) Suppose X and Y both take values in the set {0, 1} and they are jointly distributed so that the probability
that X = Y is 1/2, the probability that Y = 1 is 1/2, and the probability that X > Y is 1/10. What is the
probability that X = 1?
(a) .1
(b) .2
(c) .3
(d) .4
(e) .5
(10) Suppose 10% of the individuals in a certain population have blue eyes, 20% are left handed, and 5% are blue
eyed and left handed. What is the percent of the population that is neither left handed nor blue eyed?
(a) 25%
(b) 35%
(c) 55%
(d) 65%
(e) 75%
(11) You have a coin which is equally likely to be fair or weighted. If it is fair it lands Heads with probability 1/2.
If it is weighted, it will land Heads when flipped with probabillity 2/3. You flip the coin twice. What is the
probability that it lands Heads at least once?
(12) You place 10 slips of paper numbered 1 through 10 in a hat. You draw three slips at random. What is the
probability that the numbers on the slips are in succession? For example you draw 5, 6, and 7.
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