Question

a coin is flipped eight times where each flip comes up either heads or tails. how many possible outcomes: 1). are there in total? 2). contain exactly three heads? 3). contain at least three heads? 4). contain the same number of heads and tails?

Answer 1

There are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are: 2⁸ = 256

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination:

To get exactly 3 heads,

n=8 and r=3

(⁸C₃ ) = 8! / 3!(5!) = 56.

Therefore, there are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

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