16

Take the task of creating possible outcomes and break it into stages.

Stage 1: Select an outcome for flip #1
There are 2 possible outcomes: heads or tails
So, we can complete stage 1 in 2 ways

Stage 2: Select an outcome for flip #2
There are 2 possible outcomes: heads or tails
So, we can complete stage 2 in 2 ways

Stage 3: Select an outcome for flip #3
We can have heads or tails. So, we can complete stage 3 in 2 ways

Stage 4: Select an outcome for flip #4
We can have heads or tails. So, we can complete stage 4 in 2 ways

Stage 5: Select an outcome for flip #5
This flip MUST be heads
So, we can complete stage 5 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages in (2)(2)(2)(2)(1) ways (= 16 ways)

Answer: 16

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

RELATED VIDEO

This problem utilizes the fundamental counting principle, which states that the total number of choices is equal to the product of the independent choices. For the first flip, there are 2 options: heads or tails.

Similarly, for the second flip, there 2 options; for the third, there are 2 options; for the fourth, there are 2 options; and for the fifth there is only one option because the problem restricts this final flip to heads. Therefore, the total number of outcomes is (2)(2)(2)(2)(1) = 16. A good rephrasing of this question is, “How many different outcomes are
there if the coin is flipped 4 times?” The fifth flip, having been restricted to heads, is irrelevant.

Therefore, the total number of ways to flip the coin five times with heads for the fifth flip is equal to the total number of ways to flip the coin four times; either way, the answer is 16.
_________________

Given that A coin is flipped 5 times and we need to find how many distinct outcomes are possible if the last flip must be heads?

In each toss we have two choices -> Heads or Tails

For each of the first four outcomes we have 2 choices each => 2 * 2 * 2 * 2 = 16 ways

For the fifth toss we have only one choice as we are getting Heads

=> Total choices = 16 * 1 = 16

So, Answer will be 16
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

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