Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following experiment.Step 1. Fli...
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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) ____________.
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) ____________.
Correct answer is '0.33'. Can you explain this answer?
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Verified Answer
Consider the following experiment.Step 1. Flip a fair coin twice.Step ...
1st time it is 0.25(1/4), when tail tail comes, entire process gets repeated, so next time probability of Y to happen is 0.25*0.25 ((1/4)*(1/4)), likewise it goes on as infinite GP
Sum of infinite GP = a/(1-r)
here a= 1/4 and r = 1/4
so answer becomes 1/3 i.e 0.33
Sum of infinite GP = a/(1-r)
here a= 1/4 and r = 1/4
so answer becomes 1/3 i.e 0.33
Answer should be 0.33 P(TH)=1/4
P(HH + HT)=1/2
now if TT comes then toss again,
So, P(TTTH)= 1/16 . and so on.... P(TH+TTTH+........) = 1/4 + 1/16+... = 1/3
P(HH + HT)=1/2
now if TT comes then toss again,
So, P(TTTH)= 1/16 . and so on.... P(TH+TTTH+........) = 1/4 + 1/16+... = 1/3
Most Upvoted Answer
Consider the following experiment.Step 1. Flip a fair coin twice.Step ...
Understanding the Experiment
The experiment involves flipping a fair coin twice and checking the outcomes. There are four possible outcomes from two flips:
- (HEADS, HEADS)
- (HEADS, TAILS)
- (TAILS, HEADS)
- (TAILS, TAILS)
Calculating Probabilities
Each outcome has an equal probability of occurring since the coin is fair:
- P(HEADS, HEADS) = 1/4
- P(HEADS, TAILS) = 1/4
- P(TAILS, HEADS) = 1/4
- P(TAILS, TAILS) = 1/4
Output Conditions
- Output **Y** if the outcome is (TAILS, HEADS).
- Output **N** if the outcomes are (HEADS, HEADS) or (HEADS, TAILS).
- If the outcome is (TAILS, TAILS), the experiment restarts.
Results from Each Outcome
- **Y**: Only from (TAILS, HEADS) with a probability of 1/4.
- **N**: From (HEADS, HEADS) and (HEADS, TAILS), totaling 1/4 + 1/4 = 1/2.
- **Repeat**: From (TAILS, TAILS) with a probability of 1/4.
Considering Repeats
When (TAILS, TAILS) occurs, the experiment repeats, which means we need to account for the infinite possible trials.
Let \( p \) be the probability of eventually outputting **Y**. The equation can be set up as:
\[ p = P(TAILS, HEADS) + P(TAILS, TAILS) \cdot p \]
Substituting values:
\[ p = \frac{1}{4} + \frac{1}{4} \cdot p \]
Solving for \( p \):
\[ p - \frac{1}{4}p = \frac{1}{4} \]
\[ \frac{3}{4}p = \frac{1}{4} \]
\[ p = \frac{1}{3} \approx 0.33 \]
Final Output
Thus, the probability that the output of the experiment is **Y** is approximately **0.33**.
The experiment involves flipping a fair coin twice and checking the outcomes. There are four possible outcomes from two flips:
- (HEADS, HEADS)
- (HEADS, TAILS)
- (TAILS, HEADS)
- (TAILS, TAILS)
Calculating Probabilities
Each outcome has an equal probability of occurring since the coin is fair:
- P(HEADS, HEADS) = 1/4
- P(HEADS, TAILS) = 1/4
- P(TAILS, HEADS) = 1/4
- P(TAILS, TAILS) = 1/4
Output Conditions
- Output **Y** if the outcome is (TAILS, HEADS).
- Output **N** if the outcomes are (HEADS, HEADS) or (HEADS, TAILS).
- If the outcome is (TAILS, TAILS), the experiment restarts.
Results from Each Outcome
- **Y**: Only from (TAILS, HEADS) with a probability of 1/4.
- **N**: From (HEADS, HEADS) and (HEADS, TAILS), totaling 1/4 + 1/4 = 1/2.
- **Repeat**: From (TAILS, TAILS) with a probability of 1/4.
Considering Repeats
When (TAILS, TAILS) occurs, the experiment repeats, which means we need to account for the infinite possible trials.
Let \( p \) be the probability of eventually outputting **Y**. The equation can be set up as:
\[ p = P(TAILS, HEADS) + P(TAILS, TAILS) \cdot p \]
Substituting values:
\[ p = \frac{1}{4} + \frac{1}{4} \cdot p \]
Solving for \( p \):
\[ p - \frac{1}{4}p = \frac{1}{4} \]
\[ \frac{3}{4}p = \frac{1}{4} \]
\[ p = \frac{1}{3} \approx 0.33 \]
Final Output
Thus, the probability that the output of the experiment is **Y** is approximately **0.33**.
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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) ____________.Correct answer is '0.33'. Can you explain this answer?
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