Probability

If A and B are independent events, and P(A)=.4, P(B)=.5, and P(A $\cap$  B)=.2, find P(A l B).

• 0.4

• 0.6

• 0.2

• 0.8

Find the probability of selecting at least one person with green eyes in a sample of 5 people if it is known that 31% of people have green eyes.

• 0.997

• 0.976

• 0.671

• 0.844

If two events are mutually exclusive

• they occur at the same time

• they cannot occur simultaneously

• they are independent

Given that 52% of the U.S. population are female and 15% are older that age 65, can we conclude that (0.52)(0.15)= 7.8% are women older than age 65?

• Yes, by the multiplication rule.

• Yes, by conditional probabilities.

• No, because the events are not mutually exclusive.

• No, because the events are not independent.

Suppose you toss a fair coin ten times and it comes up heads every time. Which of the following is a true statement?

• The probability that the next toss will again be heads is 0.5.

• The law of large numbers tells how many tosses will be necessary before the percentages of heads and tails are again in balance.

• By the law of large numbers, the next toss is more likely to be tails than another heads.

• By the laws of conditional probability, the next toss is more likely to be heads given that ten tosses in a row have been heads.

Given that P(E)=0.32, P(F)=0.15, and P(E $\cap$  F)=0.048, which of the following is a correct conclusion?

• E and F are both independent and mutually exclusive.

• E and F are neither independent nor mutually exclusive.

• E and F are mutually exclusive but not independent.

• E and F are independent but not mutually exclusive.

Suppose that 68% of graduates from Germantown go to a 4-year college, 14% go to a 2-year college, 3% go into the military, 10% go into employment, and 5% search for a job. If a randomly selected student is NOT going into employment, what is the probability that he will be going to a 2-year college?

• .90

• .140

• 0.156

• 0.714

What is the probability of guessing at least one question correctly on a test with 5 true/false questions?

• 0.352

• 0.969

• 0.500

• 0.898

The law of large numbers states that

• mutually exclusive events are always dependent

• disjoint events can never occur simultaneously

• simulation is a process that can be used with 25 trials

• in the long run, the cumulative relative frequency of an event tends to the theoretical probability of an event