Fair Coin Probability

Probability is the likelihood of the occurrence of an event. The probability of event A is written P(A). Probabilities are always numbers between 0 (impossible) and 1 (possible), inclusive. Set
of possible outcomes of a particular experiment is called as event. The set of all possible outcomes of an experiment is referred to as sample space. Fair coins has same probability of heads and
tails. In this lesson we will discuss about probability problems using fair coin.

Fair Coin Probability - Example Problems

Example 1: Three fair coins are tossed simultaneously, what is the probability of getting more than one heads or more than one tails?.

Solution:

Let S = sample space, n(S) = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = 8

A be the event of getting more than one heads, n(A) = {HHH, HHT, HTH, THH} = 4

B be the event of getting more than one tails, n(B) = {HTT, THT, TTH, TTT} = 4

P(A) = `(n(A))/(n(S))` =` 4/8` = `1/2`

P(B) = `(n(B))/(n(S))` = `4/8` = `1/2`

P(A or B) = P(A) + P(B) = `1/2` + `1/2` = 1

P(A or B) = 1

Example 2: Three fair coins are tossed simultaneously, what is the probability of getting exactly two heads or exactly two tails?.

Solution:

Let S = sample space, n(S) = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = 8

A be the event of getting exactly two heads, n(A) = {HHT, HTH, THH} = 3

B be the event of getting exactly two tails, n(B) = {HTT, THT, TTH} = 3

P(A) = `(n(A))/(n(S))` =`3/8`

P(B) = `(n(B))/(n(S))` = `3/8`

P(A or B) = P(A) + P(B) = `3/8` + `3/8` = `3/4`

P(A or B) = `3/4`

Fair Coin Probability - Practice Problems

Problem1: Three fair coins are tossed simultaneously, what is the probability of getting at least one head?

Problem 2: Three fair coins are tossed simultaneously, what is the probability of getting at least two tails?.

Answer: 1) `7/8` 2) `1/2`