1. Certain data obtained from a study of a group of 1000 subscribers to a certain magazine
relating to their sex, marital status, and education were reported as follows: 312 males,
470 married, 525 college graduates, 42 male college graduates, 147 married college
graduates, 86 married males, and 25 married male college graduates. Is this data
consistent? Justify your answer.
2. A small college consists of 25% Westerners, 50% Midwestemers, and 25% Easterners. If
30% of the Westerners wear ties, 45% of the Midwestemers wear ties, and 60% of the
Easterners wear ties, what is the probability that a randomly-found tie belongs to an
3. An urn contains balls of 4 different colors, each color being represented by the same
number of balls. Four balls are drawn, with replacement. What is the probability that at
least 3 different colors are represented in the sample?
4. Consider four cards, on each of which is marked off a sidel and side 2. On card 1, both
side 1 and side 2 are colored red. On card 2, both side 1 and side 2 are colored black. On
card 3, side 1 is colored red and side 2 is colored black. On card 4, side 1 is colored black
and side 2 is colored red. A card is chosen at random. What is the probability that if one
side of the card is colored red, the other side of the card will be black?
5. From a pack of 52 cards an even number is drawn. What is the probability that half of the
cards will be red and half will be black?
6. Consider 5 families, each consisting of 4 persons. If it is reported that 6 of the 20
individuals in these families have a contagious disease, what is the probability that at
least 3 of the families will be quarantined?
7. Urn I contains 6 white balls and 4 black balls. Urn II contains 2 white and 2 black balls.
From Urn I 2 balls are transferred to Urn II. A sample of size 2 is then drawn without
replacement from Urn II. What is the probability that the sample will contain exactly 1
8. Each of 3 boxes, identical in appearance, has 2 drawers. Box A contains a gold coin in
each drawer; Box B contains a silver coin in each drawer; Box C contains a gold coin in
drawer 1 and a silver coin in the other. A box is chosen, one of its drawers is opened, and
a silver coin is found. What is the probability that the other drawer contains a gold coin?
9. Two athletic teams play a series of games where the first team winning 4 games is the
winner. The World Series is an example. Suppose that 1 of the teams is stronger than the
other and has probability p of winning each game, independent of the outcomes of any
other games. Assume that a game cannot end in a tie. Find the four probabilities that the
series will end in
a. 4,5,6, or 7 games given that p=2/3. - ^^
b. 4,5,6, or 7 games given that p= 1/2.
10. a. Suppose that in a random sample of 5 cards, taken from a regular 52-card deck, one
card is known to be an ace. What is the probability that the remaining 4 cards comprise at
least one more ace?
b. Now suppose that in that 5 card sample, one is known to be the Ace of Spades. What is
the probability that the remaining 4 cards comprise at least one more ace?
|Due By (Pacific Time)||04/23/2014 10:00 pm|
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