Fair Coin

 Probability is the likelihood of the occurrence of an event. One or more possible outcomes of a particular experiment is called event. The set of all possible outcomes of an experiment is referred to as sample space. Fair coins have same probability of heads and tails. For example, a coin is tossed once, the probability of getting a head is `1/2` , and also the probability of getting a tails is `1/2` .

 

Fair Coin - Example Problems

 

Example 1: If two fair coins tossed simultaneously, what is the probability of getting at least one head or at least two tail?

 

Solution:

Let S be the sample space, S = {HH, HT, TH, TT}, n(S) = 4

A be the event of getting at least one head, A = {HH, HT, TH}, n(A) = 3

B be the event of getting at least two tail, B = {TT}, n(B) = 1

P(A) = `(n(A))/(n(S))` =`3/4`

P(B) = `(n(B))/(n(S))` = `1/4`

P(A or B) = P(A) + P(B) = `3/4` + `1/4` = `4/4` 1

P(at least one head or at least two tail) = 1 

 

 

 

Example 2: If three fair coins tossed simultaneously, what is the probability of getting at most two heads or at most two tails?

 

Solution:

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

A be the event of getting at most two heads, A = {HHT, HTH, THH, HTT, THT, TTH, TTT} = 7

B be the event of getting at least two tails, B = {HHH, HHT, HTH, THH, HTT, THT, TTH} = 7

P(A) = `(n(A))/(n(S))` =`7/8`

P(B) = `(n(B))/(n(S))` = `7/8`

P(A or B) = P(A) + P(B) = `7/8` + `7/8` = `7/4`

P(at most two heads or at most two tails) = `7/4`

 

Fair Coin - Practice Problems

 

Problem1: If two fair coins tossed simultaneously, what is the probability of getting at most one head?

Problem 2: If three fair coins tossed simultaneously, what is the probability of getting at most two tail?

Answer: 1) `3/4` 2) `7/8`