# Discrete Mathematics Probability - 21136

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What is the probability that a five card poker hand contains the ace of hearts?

Section 6.1: #22

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 3?

Section 6.1: #24

Find the probability of winning the lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding

a) 30

b) 36

c) 42

d) 48

Section 6.2: #2

Find the probability of each outcome when a loaded die is rolled, if a 3 is twice as likely to appear as each of the other five numbers on the die.

Section 6.2: #6

What is the probability of these events when we randomly select a permutation of {1, 2, 3}?

a) 1 proceeds 3.

b) 3 proceeds 1.

c) 3 proceeds 1 and 3 proceeds 2.

Section 6.2: #24

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails?

Section 6.3: #2

Suppose that E and F are events in a sample space and p(E) = 2/3, p(F) = ¾, and p(F?E) = 5/8. Find p(E?F).

Section 6.3: #6

When a test for steroids is given to soccer players, 98% of the players taking steroids test positive and 12% of the players not taking steroids test positive. Suppose that 5% of the soccer players take steroids. What is the probability that a soccer player who tests positive takes steroids?

Section 6.3: #18

Suppose that a Bayesian spam filter is trained on a set of 500 spam messages and 200 messages that are not spam. The word “exciting” appears in 40 spam messages and in 25 messages that are not spam. Would an incoming message be rejected as spam if it contains the word “excited” and the threshold for rejecting spam is 0.9?

Section 6.4: #2

What is the expected number of heads that come up when a fair coin is flipped 10 times?

Section 6.4: #4

A coin is biased so that the probability a head comes up when it is flipped is 0.6. What is the expected number of heads that come up when it is flipped 10 times?

Section 6.4: #12

Suppose that we roll a die until a 6 comes up.

a) What is the probability that we roll the die n times?

b) What is the expected number of times we roll the die?

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