Question

Discrete Mathematics Probability Worksheet Name __________________________________________

(1) Two ordinary dice are rolled. Find the probability that ...

(a) ... the sum of the dice is 6, 7 or 8.

(b) ... the sum of the dice is 5 or at least one of the dice shows a 5

.(c) ... the two dice match.

(2) A card is drawn from an ordinary deck of 52 cards. Find the probability that the card is ...

(a) ... an ace or a heart

.(b) ... an ace or a black card

.(c) ... a diamond, a club, or a king.

(3) Two cards are drawn from deck, with replacement. (This means that one person chooses a card,looks at it and returns it, and then another person chooses a card, looks at it, and returns it.) What is the probability that ...

(a) ... the first card is an ace and the second card is black?

(b) ... both cards are spades?

(c) ... neither card has a value from {2, 3, 4, 5}?(d) ... at least one card is an ace?

(e) ... the first card is an ace or the second card is black?

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles are pulled out at once (i.e. with no particular order). What is the probability that ...

(a) ... all four marbles are red?

(b) ... more of the marbles are green than red?

(c) ... both red and green marbles are present?

(d) ... two of the marbles chosen are both labeled "5"?

(5) What is the probability that a five card hand dealt from a standard deck of cards will include fourcards of the same value? (This kind of hand is called a "four of a kind" in Poker.)

(6) A fair coin is tossed ten times in a row.

(a) What is the probability that "heads" comes up exactly five times?

(b) What is the probability that "heads" come up at least eight times?

(c) What is the probability that "heads" come up at least once?

You flip a coin 8 times. What is the probability of seeing exactly four tails?

128/256

186/256

70/256

4/256

(7) Let's say the probability of having a particular cancer is 1%.There is a test for this cancer. It will test positive 90% of the time if you have the cancer and it will correctly come out negative 80% of the time if you don't have the cancer.

Fill out the following probabilities:

Pr(cancer) = 0.01

Pr(no cancer) =

Pr(positive | cancer) = 0.9

Pr(negative | cancer) =

Pr(positive | no cancer) =

Pr(negative | no cancer) = 0.8

(8) By the product rule, the probability of the test coming out positive and you have cancer is:

Answer 1