1)Define and give examples of each of the following:

  1. Theoretical Probability
  1. Experimental Probability
  1. Independent Events
  1. Dependent Events
  1. Events that are mutually exclusive
  1. Events that are NOT mutually exclusive

2)What is the Law of Large Numbers?

3)You roll a die and flip a coin.

  1. List the sample space.
  1. Find the probability of:
  1. Flipping a head:
  1. Rolling an even number and flipping a tail
  1. Rolling a number greater than four or flipping a head.

4)A random sample of 250 working adults found that 37% drive a truck to work, 36% drive a red vehicle to work, and 12% drive a red truck. What is the probability that a person is randomly picked and they drive a truck OR a red vehicle?

5)You select two cards from a standard deck. Find the probability of:

  1. Selecting a four, not replacing the card, and then selecting a jack.
  1. Selecting an ace, replacing the card, and then selecting a heart.

6)Decide whether the following are independent or dependent events:

  1. Picking a four and picking a queen without replacement.
  1. Tossing a coin and getting a tail, and then rolling a six-sided die and getting a 4.
  1. Cubes are numbered between 1 and 50 and put into a basket. A cube is chosen,returned, and then a second numbered cube is selected from the bin.

7)The probability of choosing a battery that works is 65%. Three batteries are chosen at random.

  1. ______Find the probability that all three work.
  1. ______Find the probability that all three batteries do not work.

8)A 16-sided die is numbered 1-16. Find the probability that the roll results in an odd number or a number less than 4.

9)Use the chart below to answer the following questions:

Men / Women / Total
Play sports / 176 / 162 / 338
Does not play sports / 113 / 102 / 215
Total / 289 / 264 / 553
  1. P(S) = b. P(S|W) = c. P(S ∩ W) =

d. P( S U M) = f. P (W | S) = d. P( W ∩ W) =

10)Twenty horses are running in a race. In how many ways can they finish first, second, and third?

11)Five players on a basketball team must choose a player on the opposing team to defend. In how many ways can they choose their defensive assignment?

12)From a group of 45 people, a choir of 16 people is selected. In how many different ways can a choir of 16 people be selected?

13)A batch of 350 raffle tickets contains four winning tickets. You buy four tickets. What is the probability you have:

  1. No winning tickets.
  1. All winning tickets.
  1. You have 1 winning ticket.

14)An instant lottery game gives you probability 0.02 of winning on any one play. Plays are independent of each other. If you play ten times, what is the probability that you win at least once?

15) Given P(A) = .45, P(B) = .27, and P(A and B) = .13, find P(A or B).

16)Use the random digits tables below to simulate finding the probability of getting at least two girls in a family of five children. Describe the trials, conduct 20 trials, and estimate the probability based on your results.