STATISTICS AND PROBABILITY

1. PERFORMANCE TASK 1
RANDOM VARIABLES

2. A. Find the possible values of the random
variable described in each situation.
1. Two balls are drawn in succession without replacement from an urn containing 4
red balls and 5 blue balls. Let R be the random variable representing the number
of red balls. Find the values of the random variable R.
2. In a hospital, a statistician records the sex of newborn babies. Let M be the
random variable representing males among five newborn babies.
3. Let Z be a random variable representing the result of rolling a die.
4. Four coins are tossed. Let T be the random variable representing the number of
tails that occur. Find the values of the random variable T.
5. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in
succession. Each ball is placed back in the box before the next draw is made. Let
G be a random variable representing the number of green balls that occur. Find
the values of the random variable G.

3. B. Choose the letter that corresponds to the
correct answer.
1.Which of the following is a discrete random variable?
a. The stained area of the floor when a glass of
coffee spills on it
b. The time in seconds that a runner completes a
200-meter race
c. The exact mass of a buko pie made by a baker
d. The number of customers each day in computer
shop

4. B. Choose the letter that corresponds to the
correct answer.
2. Which of the following is NOT a true statement?
a. Random variables can only have one value.
b. The value of a random variable could be
zero.
c. A random variable cannot be negative.
d. A random variable can be discrete or
continuous.

5. B. Choose the letter that corresponds to the
correct answer.
3. Three coins are tossed at once, which are
possible values of the random variable for the
number of coins that match?
a.{0,1}
b.{1,2}
c.{2,3}
d.{3}

6. B. Choose the letter that corresponds to the
correct answer.
4. You decide to conduct a survey of families with two
children. You are interested in counting the number of girls
(out of 2 children) in each family. Is this a random variable,
and if it is, what are all its possible values?
a. yes, it is a random variable, and its values can be 1 or 2
b. yes, it is a random variable, and its values can be 0, 1 or 2
c. yes, it is a random variable, and its values can be 2 or 4
d. No, it is not a random variable, since it is not random

7. B. Choose the letter that corresponds to the
correct answer.
5. Which of the following is a continuous random
variable?
a. The number of eggs that a hen lay in a day
b. The number of people watching an Inter-town
basketball game
c. The average weight of male athletes
d. The amount of paint used in painting clay pots

8. C. Present five (5) pictures in which you can
extract the types of random variables.
What makes it discrete?
continuous?

9. PERFORMANCE 2: PROBABILITY DISTRIBUTION
Last school year 2022-2023 in
Pinoma National High School, 6 days
were allotted for the enrolment of
Grade 11. The enrolment was from
Grade 8-12 noon for 6 days.

10. PERFORMANCE 2: PROBABILITY DISTRIBUTION
Below is the table showing the
number of enrollees in each day.
Day Monday Tuesday Wednesday Thursday Friday Saturday
Number of
Students (x) 79 40 50 43 40 20

11. PERFORMANCE 2: PROBABILITY DISTRIBUTION
b. What is the probability of the
day which has the highest number
of enrolees?
Day Monday Tuesday Wednesday Thursday Friday Saturday
Number of
Students (x) 79 40 50 43 40 20

12. PERFORMANCE 2: PROBABILITY DISTRIBUTION
c. What is the mean and variance of
the probability distribution?
Day Monday Tuesday Wednesday Thursday Friday Saturday
Number of
Students (x) 79 40 50 43 40 20