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Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails.

P(E) + P(E¯) = 1, where E and E¯ are complementary events.

The event E¯, representing ‘**not E**‘, is called the **complement** of the event **E**.

**Example: 1**

What is the probability of drawing a heart from a deck of cards?

**Solution:**

There are total 52 cards in a deck out of which 13 cards are of heart.

So the favourable outcomes are 13 and the total no. of events is 52.

**Example 2**

If we toss two coins together, then what is the probability of getting at least one head ?

**Solution:**

If we toss two coins together then the total outcomes could be The favourable outcomes for at least one head will be

P (for at least one head) =

**Example 3**

Find the probability that a leap year selected randomly will have 53 Sundays?**Solution**

No. of days in a leap year = 366 days = 52 weeks + 2 days

It implies a leap year will have 52 Sundays. In remaining 2 days, possible outcomes are:

Sun, Mon

on, Tue

Tue, Wed

Wed, Thu

Thu, Fri

Fri, Sat

Sat, Sun

Total out comes = 7 Favourable outcomes that Sunday will come in these two days = 2

Required probability =

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