If three fair coins are tossed find the probability of each

If three fair coins are tossed, find the probability of each number of heads. 0 1 2 3 1 or 2

Solution

When we toss three coins simultaneously then the possible of outcomes are: (HHH) or (HHT) or (HTH) or (THH) or (HTT) or (THT) or (TTH) or (TTT) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 2³ = 8=n(S)

Let E= event of getting heads

The above explanation will help us to solve the problems on finding the probability of tossing three coins.

1.0 means no head

P(no heads) = P(E) = n(E)/n(S) = 1/8.

2.1 means getting one head

Let E = event of getting 1 head. Then,
E = {HTT, THT, TTH} and, therefore,
n(E) = 3.
Therefore, P(getting 1 head) = P(E) = n(E)/n(S) = 3/8

3. getting 2 heads

Then,
E = {HHT, THH, HTH} and, therefore,
n(E) = 3.
Therefore, P(getting 2 head) = P(E) = n(E)/n(S) = 3/8

4.getting 3 heads

E = {HHH}
and, therefore, n(E) = 1.
Therefore, P(getting all heads) = P(E) = n(E)/n(S) = 1/8.