Question

A coin is tossed 2 times and the outcomes are recorded. How many possible outcomes are there?

Answer 1

Hint: When we toss an unbiased coin, the sample space consists of 2 elements. Those two are Head and Tail. So, the number of possible outcomes is 2. Therefore, the probability of getting a head by tossing a coin is 1/2 and same as that of getting a tail.

Complete step-by-step answer:
As per the given question, a coin is tossed 2 times and its outcomes are recorded.
For the first time tossing possible outcomes are either a head or a tail.
So, let's divide into two cases:
Case(1): Head is the outcome. Now, lets go to second toss which is further divided into two cases:
Case(1(a)): Head is the outcome. And, now in the last toss also we have two cases:
Case(1(a(i))): Head is the outcome.
Case(1(a(ii))): Tail is the outcome.

Case(1(b)): Tail is the outcome. And, now in the last toss also we have two cases:
Case(1(b(i))): Head is the outcome.
Case(1(b(ii))): Tail is the outcome.

So, in total we have 4 cases as shown in the table below.

1st Toss	2nd Toss
Head	Head
Head	Tail
Tail	Head
Tail	Tail

Hence, the number of possible outcomes is 4.

Note: While solving these types of questions carefully analyze the problem. If the number of times the coin is tossed is n, then the number of possible outcomes is . As we are tossing the coin each time, we have 2 possible outcomes, so we keep multiplying into 2 for each toss.