# Chance in everyday situations · Grade 10 · 3 units

> Chance in everyday situations, Grade 10 · 3 units: Deciding by chance and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Chance in everyday situations (Grade 10 · 3 units) you practise 4 skills: Probability by counting · Complements and disjoint events · Events in two stages in a table · Deciding by chance.

When every outcome is equally likely, the probability of an event is the number of outcomes that fit divided by the number of all the outcomes. A probability is always between 0 and 1.

Two disjoint events cannot happen together, so the probability that one of them happens is the sum of their probabilities. The complement of an event is that it does not happen, and its probability is 1 minus the probability of the event.

For an experiment in two stages, draw a table: the first stage down the side, the second across the top, and each box is one outcome. Count the boxes that fit and divide by the number of all the boxes.

To decide between two options, compare their probabilities. The expected number of times an event happens is the number of trials times the probability.

**Tip:** Before you work anything out, count all the outcomes: that is the denominator of the fraction.

## What you learn

### Probability by counting

- Example: A bag contains 9 red balls and 2 blue balls. One ball is taken out without looking. What is the probability of taking out a red ball?
- Answer: 9/11
- Solution: There are 11 balls in the bag, and 9 of them are red. The probability is: 9/11

### Complements and disjoint events

- Example: The probability that the team will win the match is 6/7 . What is the probability that the team will not win the match?
- Answer: 1/7
- Solution: 1 − 6/7 = 7/7 − 6/7 = 1/7

### Events in two stages in a table

- Example: Two coins are tossed. The table shows every possible result: the first coin down the side, the second across the top. (A table of the results of two coins) What is the probability that both coins show tails? Write it in lowest terms.
- Answer: 1/4
- Solution: The table has 4 boxes, and 1 fits . The probability: 1/4

### Deciding by chance

- Example: A bag contains 8 red balls, 2 blue balls and 4 green balls. One ball is taken out without looking. Which is more likely: taking out a red ball or taking out a blue ball?
- Options: A blue ball · The same chance · A red ball
- Answer: A red ball
- Solution: The probabilities are 8/14 and 2/14 . Taking out a red ball is more likely.

## Not on the site yet

- Running experiments
- Proving the rules of probability

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 10 · 3 units topics](https://kixplo.com/il/en/math/grade-10-3u/)