Chances | Year 3 Mathematics IGCSE (Cambridge) - Class 3 PDF Download

Introduction:

In this chapter, we will learn about chances. Chances tell us how likely something is to happen. We can use words like "certain," "likely," "unlikely," and "impossible" to talk about chances. We will also learn how to compare things that are more likely, less likely, or equally likely to happen. By the end of this chapter, you'll be able to talk about chances in fun and easy ways!

1. What is a Chance?

Understanding Chances:

A chance tells us how likely something is to happen. For example, when you flip a coin, you have a chance of getting either heads or tails. Some things are very likely to happen, and some things are very unlikely!

Simple Examples:

• It’s certain that the sun will rise tomorrow. This is a certain event.
• It’s likely that you will get an apple from a basket with 9 apples and 1 orange. This is a likely event.
• It’s unlikely that it will snow in the summer. This is an unlikely event.
• It’s impossible to pick a purple apple from a basket with only red and green apples. This is an impossible event.

2. More Likely, Less Likely, and Equally Likely

• More Likely:

  If something is more likely, it means there is a bigger chance of it happening. For example, if you have 5 red marbles and 1 blue marble in a bag, it is more likely to pick a red marble because there are more red marbles.

  Example: You are more likely to roll a 3 than a 6 on a die because there are more numbers that are lower than 6.

• Less Likely:

  If something is less likely, it means there is a smaller chance of it happening. For example, if you have 1 red marble and 9 blue marbles in a bag, it is less likely to pick a red marble because there are more blue marbles.

  Example: It’s less likely to get heads on a coin flip after getting heads five times in a row.

• Equally Likely:

  If two things are equally likely, it means they have the same chance of happening. For example, when you roll a die, each of the numbers 1, 2, 3, 4, 5, and 6 is equally likely to come up because they all have the same chance.

  Example: It’s equally likely to get heads or tails when you flip a fair coin.

3. Certain, Likely, Unlikely, Impossible

• Certain:

  A certain event is one that will definitely happen. For example, the sun will rise tomorrow.

  Example: It is certain that you will get a result when you roll a die (it will land on one of the 6 sides).

• Likely:

  A likely event is one that is more likely to happen but not guaranteed. For example, it is likely that you will get a blue ball if you pick a ball from a bag that has 8 blue balls and 2 red balls.

  Example: It is likely that you will get wet if you go outside without an umbrella when it is raining.

• Unlikely:

  An unlikely event is one that is less likely to happen, but it is still possible. For example, if you roll a die, it is unlikely but still possible to roll a 6 after rolling a 1, 2, 3, 4, and 5.

  Example: It is unlikely that it will snow tomorrow in the summer.

• Impossible:

  An impossible event is one that cannot happen. For example, it is impossible to get 7 on a regular 6-sided die.

  Example: It is impossible for you to be in two places at once!

4. Word Problems with Probability

• Word Problem 1:

  You have a bag with 3 red marbles, 2 blue marbles, and 5 green marbles. What is more likely: picking a red marble or a green marble?

  Answer: It is more likely to pick a green marble because there are 5 green marbles and only 3 red marbles.
• Word Problem 2:

  You roll a six-sided die. What is the chance of rolling a 2?

  Answer: It is equally likely to roll any number from 1 to 6, so the chance of rolling a 2 is 1/6.
• Word Problem 3:

  If you have a box with 2 red balls, 1 yellow ball, and 3 green balls, what is the probability of picking a yellow ball?

  Answer: The probability of picking a yellow ball is 1/6, since there are 6 balls in total and 1 yellow ball.
• Word Problem 4:

  If you toss a fair coin, what is the probability of getting tails?

  Answer: The probability of getting tails is 1/2 because there are two possible outcomes (heads or tails), and both are equally likely.
• Word Problem 5:

  You are drawing cards from a deck. What is the chance of drawing a red card?

  Answer: There are 26 red cards in a deck of 52 cards, so the chance of drawing a red card is 26/52, which simplifies to 1/2.

5. Practice Questions:

• Which of the following events is impossible: (a) rolling a 7 on a 6-sided die, (b) getting heads on a fair coin flip, (c) picking a blue marble from a bag of red marbles?
• What is more likely: (a) picking a red ball from a bag with 8 red balls and 2 blue balls, (b) picking a green ball from a bag with 3 green balls and 4 yellow balls?
• If you roll a die, what is the chance of getting a number less than 4?
• Which is more likely: (a) winning a game with a 50% chance of winning, (b) winning a game with a 10% chance of winning?
• If you have a basket with 10 apples, 4 oranges, and 3 bananas, what is the chance of picking an orange?