Question

Suppose an experiment has 5 outcomes. Outcome 1 is twice as likely as outcome 2. Outcome 2 is twice as likely as outcome 3. Outcome 3 is twice as likely as outcome 4. Outcome 4 is twice as likely as outcome 5. Find the probability of outcome 1.

[Write your answer as a fraction. For example, 1/2 or 2/3 or 15/16, etc.]

[Hint: Call outcome 5 the "x" and write all other outcomes in terms of "x" to find the solution.]

Answer 1

Let's assign a variable to the probability of outcome 5, which is represented by "x".

According to the given information, we can express the probabilities of the other outcomes in terms of "x":

Outcome 4: The probability of outcome 4 is twice as likely as outcome 5, so it is 2x.
Outcome 3: The probability of outcome 3 is twice as likely as outcome 4, so it is 2(2x) = 4x.
Outcome 2: The probability of outcome 2 is twice as likely as outcome 3, so it is 2(4x) = 8x.
Outcome 1: The probability of outcome 1 is twice as likely as outcome 2, so it is 2(8x) = 16x.

To find the probability of outcome 1, we need to sum up the probabilities of all outcomes, which should equal 1:

x + 2x + 4x + 8x + 16x = 1

Simplifying the equation:

31x = 1

Dividing both sides by 31:

x = 1/31

Therefore, the probability of outcome 1 is 16x, which is 16 * (1/31) = 16/31.

Answer 2

Thanks so much for this wonderful explanation.