Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If…
2016
Consider the following experiment.
Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places) _____ .
Attempted by 58 students.
Show answer & explanation
Correct answer: 0.33 to 0.34
Let p be the probability the experiment outputs Y.
TAILS, HEADS occurs with probability 1/4 and leads to output Y.
HEADS, HEADS occurs with probability 1/4 and leads to output N.
HEADS, TAILS occurs with probability 1/4 and leads to output N.
TAILS, TAILS occurs with probability 1/4 and causes the process to restart (so the same p applies thereafter).
Therefore p satisfies the equation p = 1/4 + (1/4)·p.
Solving gives (3/4)·p = 1/4, so p = 1/3 ≈ 0.33 (to two decimal places).