Ch 5 Probability

When two coins are tossed, the probability of getting two heads is 0.25. This means that

• of every 100 tosses, exactly 25 will have two heads.
• the odds against two heads are 4 to 1.
• in the long run two heads will occur on 25% of all tosses of two coins.
• if you get two heads on each of the first five tosses of the coins, you are unlikely to get heads the fourth time.

You are playing a board game with some friends that involves rolling two six-sided dice.  For eight consecutive rolls, the sum on the dice is 6.  Which of the following statements is true?

• Each time you roll another 6, the probability of getting yet another 6 on the next roll goes down.
• Each time you roll another 6, the probability of getting yet another 6 on the next roll goes up.
• You should find another set of dice:  eight consecutive 6’s is impossible with fair dice.
• The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.

A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening on the grounds that after many bad hands he is due for a winner.

• He's right, because the winnings have to average out.
• He's wrong, because successive deals are independent of each other.
• He's right, because successive deals are independent of each other.
• He's wrong, because he’s clearly on a “cold streak.”

An assignment of probabilities must obey which of the following?

• The probability of any event must be a number between 0 and 1, inclusive.
• The sum of all the probabilities of all outcomes in the sample space must be exactly 1.
• The probability of an event is the sum of the probabilities of outcomes in the sample space in which the event occurs.
• All three of the above.

Event A has probability 0.4. Event B has probability 0.5.   If A and B are mutually exclusive, then the probability that both events occur is

• 0.0
• 0.1
• 0.9
• 0.7

Event A has probability 0.4. Event B has probability 0.5.   If A and B are independent, then the probability that both events occur is

• 0.0
• 0.1
• 0.9
• 0.2

Students at University X must have one of four class ranks—freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a University X student is selected at random, the probability that he or she is either a junior or a senior is

• 30%
• 35%
• 65%
• 70%

Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.
The probability that the next five babies are girls is

• 1.0
• 0.5
• 0.03125
• 0.0625

Suppose that A and B are independent events with P(A) = 0.2 and P(B) = 0.4. P(A OR B) is:

• 0.08
• 0.12
• 0.52
• 0.60

Event A occurs with probability 0.6. The conditional probability that event B occurs, given that A occurs, is 0.5. The probability that both A and B occur

• 0.3
• 0.11
• 0.625
• 0.1