Understand the Statistics, Data Analysis, and Probability Section of the California High School Exit Exam: Math

There are 12 problems involving statistics, data analysis, and probability on the CAHSEE. These problems are grouped together. Here are some samples with suggested approaches.
  1. The Chicago Bulls scored 98, 110, 112, and 120 points in four consecutive games. What is the mean score for the Chicago Bulls in these four games?

    1. 110

    2. 112

    3. 120

    4. 440

    Underline the key words mean score. Now that you know what you are looking for, pull out important information.

    98, 110, 112, 120

    To find the mean score, you must find the total of the scores and then divide that total by the number of games played.

    98 + 110 + 112 + 120 = 440 total points

    Since four games were played, divide 440 by 4, giving a mean score of 110. The correct answer is A.

  2. John divides his monthly paycheck like this:

    25% entertainment

    20% in the bank

    20% car and bike repair

    15% his hobby

    10% miscellaneous items

    10% school supplies

    If John receives $100 on this month's paycheck, how much does he put in the bank?

    1. $2

    2. $20

    3. $35

    4. $60

    To answer this question, you must again read the graph carefully and apply some simple math. John puts 20% of his income in the bank. Twenty percent of $100 is $20. So, he puts $20 in the bank. The correct answer is B.

  3. Three green, four red, and seven yellow marbles are placed in a bag. If a yellow marble is selected first and not replaced in the bag, what is the probability of selecting a yellow marble on the second draw?

    1. 3/7

    2. 4/7

    3. 1/2

    4. 6/13

    First, focus on what you are looking for, probability of a yellow marble on the second draw. Since there are a total of 14 marbles and 7 are yellow, then the probability of selecting a yellow marble on the first draw is 7/14. If a yellow marble is selected on the first draw, then 6 yellow marbles are left out of 13 total marbles. The correct answer is D, 6/13.

  4. Brenda is at a baseball hat store. In this store, there are only five different choices for hat color: red, orange, yellow, green, and blue. There are only four different choices for teams: Dodgers, Indians, Yankees, and Cubs. Each team hat is made in each color. If Brenda is handed a hat from the store at random, what is the probability that it is an orange Cubs hat?

    1. 1/25

    2. 1/20

    3. 1/5

    4. 1/4

    You are looking for an orange Cubs hat. The probability that the hat is orange is 1/5. The probability that the hat is a Cubs hat is 1/4. To find the probability that the hat is both an orange hat and a Cubs hat, you multiply the probability of each, 1/4 times 1/5 equals 1/20, because these are independent probabilities. Therefore, you know that the probability that the hat is an orange Cubs hat is 1/20. The correct answer is B.

  5. Bob Newhart is the host of a game show that has four contestants. Bob has four cards behind his back. One is blue, one is green, one is yellow, and one is orange. Each contestant can make only one selection and must keep that selection. The contestant who selects the green card wins a new sports car. The first contestant, Koji, selects a card. If the card he selects is yellow, what is the probability that the second contestant, Keiko, wins the new sports car?

    1. 1/8

    2. 1/4

    3. 1/3

    4. 1/2

    To answer this question, you must follow the information given carefully.

    When Koji picks a card, the probability of his getting the green card is 1/4. Since he eliminates one card that is not the green card, there are only three cards remaining, and one of them is green. Therefore, the probability that Keiko picks the green card and wins a new sports car is 1/3. The correct answer is C.

  6. A small container is filled with buttons. Each button is the same size and shape. The container has six yellow buttons, three green buttons, five blue buttons, and four brown buttons. Ricardo takes out three green buttons and does not put them back into the container. If Ricardo selects another button at random, what is the probability that the button is yellow?

    1. 1/18

    2. 1/6

    3. 2/5

    4. 3/5

    You should first focus on what you are looking for, the probability of selecting a yellow button (after the three buttons are removed). Next, pull out important information:

    6 yellow

    3 green

    5 blue

    4 brown

    Note the action in the problem — three green buttons are removed.

    Now you should carefully attack the problem.

    A total of 18 buttons are in the container at the start. If the 3 green buttons are removed, only 15 buttons remain in the container. You know that 6 are yellow, 5 are blue, and 4 are brown. Therefore, the probability of picking a yellow button out of those 15 in the container is 6/15, which reduces to 2/5. The correct answer is C.