Answer to Question #68678 in Statistics and Probability for Kenny

Question

A coin is rolled thrice, what is the probability for an event that at least two head or at least two tails occur?
(7/3)

Answer 1

Let H represent an outcome of heads and T represent an outcome of tails.
For three tosses of the coin all the possible outcomes are:
H-H-H
T-H-H
H-T-H
T-T-H
H-H-T
T-H-T
H-T-T
T-T-T
These eight possible outcomes are the sample space (2^3=8).
The probability of tossing heads at least twice can be found by looking down the list of eight possible outcomes and finding each outcome that has two or more heads in it. The outcomes are:
{H-H-H, T-H-H, H-T-H, H-H-T}.
Therefore, there are four of the eight outcomes that have two or more heads in them. The probability of throwing at least two heads in three tosses is
P(H≥2)=4/8=1/2

The probability of tossing tails at least twice can be found by looking down the list of eight possible outcomes and finding each outcome that has two or more tails in it. The outcomes are:
{T-T-H, T-H-T, H-T-T, T-T-T}.
Therefore, there are four of the eight outcomes that have two or more tails in them. The probability of throwing at least two tails in three tosses is
P(T≥2)=4/8=1/2

The probability for an event that at least two heads or at least two tails occur is
P= P(H≥2)+P(T≥2)=1/2+1/2=1