In life, we often encounter many probabilities. For example, when you are walking on a street, you may think that you will probably see a random car passing by, or you may have a possibility of tripping over a stone. In mathematics, we account these possibilities on a scale, from 0 to 1.

0 means the event is impossible to occur

1 means the event is definitely going to occur

Anything closer to 0 means the event is unlikely to occur, for example 0.1, 0.2, 0.3, 0.4

Anything closer to 1 means the event is likely to occur, for example 0.9, 0.8, 0.7

For example, when I flip a coin, what is the probability of getting a tail?

As you might have realized, in an ideal situation, it would be 0.5. Since there are only 2 possibilities, we divide 1 by 2, and we get 1/2, which is 0.5. We divide 1 because we know we are definitely going to get either tails or heads, hence the probability of getting either tails OR heads is 1.

You add up the probability when you are trying to calculate the probability of one event OR another event.

Now, if you flip two coins, what is the probability of getting a tails then a head?

Now you are trying to find out the probability of first getting a tails, and the probability of getting heads after.

Let T be tails and H be heads

Now, the probability of first getting tails is 0.5. The probability of getting a heads after is 0.5. In order to find out the probability of first getting tails AND getting a heads after, we simply multiply the probabilities. Hence, in this case it is 0.5 x 0.5 = 0.25, or 1/4.

You multiply the probabilities when you are trying to calculate the probability of one event AND another event.

Now, in many questions you may be asked to find several possible routes, for example you may be asked, in this case, the probability of getting a tail AND a head.

There are two ways of getting a tail AND a head. This includes:

Getting a tail first, then a head after

OR

Getting a head first, then a tail after.

Now, apply the rule “And = Multiply”, “Or = Add”

The probability of getting a tail first AND a head after is

1/2 x 1/2 = 1/4

The probability of getting a head first AND a tail after is

1/2 x 1/2 = 1/4

The probability of getting a tail first AND a head after OR getting a head first AND a tail after is

1/4 + 1/4 = 2/4 = 1/2, as you might have expected.