Three coins are flipped. Find the probabilities

a. p(two heads)=
b. p(at most two heads)=
c. p(no heads)=

To find the probabilities, we need to understand the possible outcomes of flipping three coins.

When flipping a single coin, there are two possible outcomes: heads (H) or tails (T).

When flipping three coins, we have a sample space of 2^3 = 8 possible outcomes:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

a. To find the probability of getting two heads (H) when flipping three coins:

We can see that there are three outcomes that have two heads: HHT, HTH, and THH.
So the probability of getting two heads is 3/8.

b. To find the probability of getting at most two heads when flipping three coins:

Getting at most two heads means getting either no heads or only one head.
We can see that there are four outcomes that meet this condition: TTT, HTT, THT, and TTH.
So the probability of getting at most two heads is 4/8 = 1/2.

c. To find the probability of getting no heads (i.e., all tails) when flipping three coins:

There is only one outcome with no heads: TTT.
So the probability of getting no heads is 1/8.