Unit E: Statistics and Probability

Chapter 2: Probability

Practice

Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.

Download File

Practice
Solutions

A survey at school found that 21 out of 28 students have an Instagram account. If there are 550 students at the school, how many students will have an Instagram account?
Robert picked some apples in an orchard. For every 17 apples picked, 2 apples had worms in them. If Robert picks 230 apples, how many of them will have worms?

Johann asked a sample of students to name their favourite type of pet. He recorded the data in a table.

Type of Pet	Number of Students
cat	8
dog	15
hamster	2
other	3
total	28

There are 325 students at Johann's school. Predict the number of students at the school whose favourite type of animal is a cat.

A manufacturer sells beads. Beads are sold in boxes of 200. Typically, 1 out of 7 beads is cracked or broken. How many extra beads should be put in each box to ensure that 200 usable beads are contained in each box?

Question 1

A survey at school found that 21 out of 28 students have an Instagram account. If there are 550 students at the school, how many students will have an Instagram account?

Solution

Step 1: Find the probability that a student has an Instagram account.

\begin{array}{rcl} probability & = & \frac{number of students with an Instagram account}{number of students in sample} \\ = & \frac{21}{28} \\ = & 0.75 \end{array}

Step 2: Substitute the probability, 0.75, and the total number of students, 550, into the formula.

\begin{array}{rcl} prediction of favourable outcomes & = & probability \times total number of outcomes \\ = & 0.75 \times 550 \\ = & 412.5 \end{array}

There will be approximately 413 students in the school that have an Instagram account.

Question 2

Robert picked some apples in an orchard. For every 17 apples picked, 2 apples had worms in them. If Robert picks 230 apples, how many of them will have worms?

Solution

Step 1: Find the probability that an apple has a worm.

\begin{array}{rcl} probability & = & \frac{number of apples with worms}{number of apples in sample} \\ = & \frac{2}{17} \\ = & 0.118 \end{array}

Step 2: Substitute the probability, 0.118, and the total number of apples picked, 230, into the formula.

\begin{array}{rcl} prediction of favourable outcomes & = & probability \times total number of outcomes \\ = & 0.118 \times 230 \\ = & 27.1 \end{array}

There will be approximately 27 apples that have a worm.

Question 3

Johann asked a sample of students to name their favourite type of pet. He recorded the data in a table.

Type of Pet	Number of Students
cat	8
dog	15
hamster	2
other	3
total	28

There are 325 students at Johann's school. Predict the number of students at the school whose favourite type of animal is a cat.

Solution

Step 1: Find the probability that a student's favourite pet is a cat.

\begin{array}{rcl} probability & = & \frac{number of students whose favourite pet is a cat}{total number of students in sample} \\ = & \frac{8}{28} \\ = & 0.286 \end{array}

Step 2: Substitute the probability, 0.286, and the number of students in the school, 325, into the formula.

\begin{array}{rcl} prediction of favourable outcomes & = & probability \times total number of outcomes \\ = & 0.286 \times 325 \\ = & 92.95 \end{array}

There are 93 students whose favourite pet is a cat.

Question 4

A manufacturer sells beads. Beads are sold in boxes of 200. Typically, 1 out of 7 beads is cracked or broken. How many extra beads should be put in each box to ensure that 200 usable beads are contained in each box?

Solution

Step 1: Find the probability that a bead will be broken.

\begin{array}{rcl} probability & = & \frac{number of broken beads}{total number of beads in sample} \\ = & \frac{1}{7} \\ = & 0.143 \end{array}

Step 2: Substitute the probability, 0.143, and the number of beads found in a box, 200, into the formula.

\begin{array}{rcl} prediction of favourable outcomes & = & probability \times total number of outcomes \\ = & 0.143 \times 200 \\ = & 28.6 \end{array}

The manufacturer should be putting at least 29 extra beads in each box.