1. Drawing a Card If one card is drawn from a deck, find the probability of getting these results.
Probability = Number of desired card / total number of cards
a. An ace: 4/52 = 1/13
b. A diamond: 13/52 = 1/4
c. An ace of diamonds: 1/52
d. A 4 or a 6: 8/52 = 2/13
e. A 4 or a club: (13+3)/52 = 16/52 = 4/13
f. A 6 or a spade: (13+3)/52 = 16/52 = 4/13
g. A heart or a club: 26/52 = 1/2
h. A red queen: 2/52 = 1/26
i. A red card or a 7: (26+2)/52 = 28/52 = 7/13
j. A black card and a 10: 2/52 = 1/26
2. Cards If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities.
P(two cards) = P(first card) x P(second card)
a. Both are spades: (13/52)*(12/51) = 1/17
b. Both are the same suit: 4*(1/17) = 4/17
c. Both are kings: (4/52)*(3/51) = 1/221
3. Selecting Cards Find the probability of getting 2 face cards (king, queen, or jack) when 2 cards are drawn from a deck without replacement.
Total number of face cards in the deck = 3*4 = 12
Probability = (12/52)*(11/51) = 11/121
4. Senate Partisanship The composition of the Senate of the 107th Congress is 49 Republicans 1 Independent 50 Democrats A new committee is being formed to study ways to benefit the arts in education.
If 3 Senators are selected at random to head the committee, what is the probability that they will all be Republicans?
P( 3 Senators) = P(1st senator) x P(2nd senator) x P(3rd senator)
P(3 republicans) = (49/100)*(48/99)*(47/98) = 0.11394
What is the probability that they will all be Democrats?
P(3 democrats) = (50/100)*(49/99)*(48/98) = 0.121212
What is the probability that there will be 1 from each party, including the Independent? Source: New York Times Almanac.
P(1 from each party) = 6*(49/100)*(1/99)*(50/98) = 0.01515
5. Winning Tickets If 50 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets.
P(win both prizes) = 2*(1/50)*(1/49) = 0.000816
6. Exercises 1 through 8 include questions that contain a flaw. Identify the flaw and rewrite the question, following the guidelines presented in this section.
1. Will you vote for John Doe for class president or will you vote for Bill Jones, the football star?
Irrelevant choices provided, as football star can’t be my class president.
Correction: Will you vote for John Doe for class president or Mike Taylor?
2. Would you buy an ABC car even if you knew the manufacturer used imported parts?
3. Should banks charge their checking account customers a fee to balance their checkbooks when customers are not able to do so?
4. Do you think that students who didn’t attend Friday’s class should not be allowed to take the retest?
There wouldn’t be a retest if students absent of Friday aren’t allowed.
Correction: Do you think that students who didn’t attend Friday’s class should be allowed to take a retest?
5. How long have you studied for this examination?
Examination is still to be conducted.
Correction: How long have you been studying for this examination?
6. Which artificial sweetener do you prefer?
No choices are provided to select one as a preference.
Correction: Which artificial sweetener do you like?
7. If a plane were to crash on the border of New York and New Jersey, where should the survivors be buried?
Dead should be buried, not the survivors.
Correction: If a plane were to crash on the border of New York and New Jersey, where should the dead be buried?
8. Are you in favor of imposing a tax on tobacco to pay for health care related to diseases caused by smoking?