# Finding probabilities

When you throw a die (plural: dice), there are six possible different outcomes. It can show either $$1$$, $${2}$$, $${3}$$, $${4}$$, $${5}$$ or $${6}$$.

But how many possible ways are there of obtaining an even number? There are three possibilities: $${2}$$, $${4}$$ and $${6}$$.

The probability of obtaining an even number is $$\frac{3}{6} (= \frac{1}{2}$$ or $$0.5$$ or $$50\%)$$

If every possible outcome has the same chance of occuring, the probability of an outcome equals the number of ways the outcome can happen divided by the total number of possible outcomes.
Question

Q1. How many outcomes are there for the following experiments? List all the possible outcomes.

a) Tossing a coin

b) Choosing a sweet from a bag containing $$1$$ red, $$1$$ blue, $$1$$ white and $$1$$ black sweet.

c) Choosing a day of the week at random.

Q2. Sindhu writes the letters of the word 'MATHEMATICS' on separate cards and places them in a bag. She then draws a card at random.

What is the probability that Sindhu chooses the letter 'A'?

A1.

a) There are two possible outcomes (head and tail).

b) There are four possible outcomes (red, blue, white and black).

c) There are seven possible outcomes (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday).

A2.

There are $$11$$ letters in MATHEMATICS, $$2$$ of which are A. So the probability that Sindhu chooses the letter A is $$\frac{2}{11}$$.