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A die is tossed thrice. Success is getting 2 or 5 on a toss. What is the variance of the number of success?
- a)1/3
- b)2/3
- c)4/5
- d)35
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A die is tossed thrice. Success is getting 2 or 5 on a toss. What is t...
P(success) = Probability of getting 2 or 5 is 2/6 = 1/3
P(failure) = Probability of not getting 2 or 5 is 4/6 = 2/3
Probability of 0 success and 3 failure is
Probability of 1 success and 2 failure is
Probability of 0 success and 3 failure is
Probability of 1 success and 2 failure is
Probability of 2 success and 1 failure is 
Probability of 3 success and 0 failure is
Probability of 3 success and 0 failure is
x is the number of success and p(x) is probability of x times success.
Most Upvoted Answer
A die is tossed thrice. Success is getting 2 or 5 on a toss. What is t...
Understanding the Problem
When a die is tossed, we define success as rolling a 2 or a 5. This gives us two successful outcomes out of six possible outcomes on a die.
Calculating Probability of Success
- The probability of success (rolling a 2 or 5) is:
- P(success) = 2 successful outcomes / 6 total outcomes = 1/3
- The probability of failure (not rolling a 2 or 5) is:
- P(failure) = 1 - P(success) = 1 - 1/3 = 2/3
Setting Up the Experiment
- The die is tossed three times, and we define the random variable X as the number of successes in these three tosses.
- Since each toss is independent, X follows a binomial distribution with parameters n = 3 (number of trials) and p = 1/3 (probability of success).
Calculating Variance
- The formula for the variance of a binomial distribution is given by:
- Variance = n * p * (1 - p)
- Substituting the values:
- Variance = 3 * (1/3) * (2/3)
- Variance = 3 * (1/3) * (2/3) = 2/3
Conclusion
The variance of the number of successes when tossing a die three times, where success is defined as rolling a 2 or 5, is indeed 2/3. Thus, the correct answer is option 'B'.
When a die is tossed, we define success as rolling a 2 or a 5. This gives us two successful outcomes out of six possible outcomes on a die.
Calculating Probability of Success
- The probability of success (rolling a 2 or 5) is:
- P(success) = 2 successful outcomes / 6 total outcomes = 1/3
- The probability of failure (not rolling a 2 or 5) is:
- P(failure) = 1 - P(success) = 1 - 1/3 = 2/3
Setting Up the Experiment
- The die is tossed three times, and we define the random variable X as the number of successes in these three tosses.
- Since each toss is independent, X follows a binomial distribution with parameters n = 3 (number of trials) and p = 1/3 (probability of success).
Calculating Variance
- The formula for the variance of a binomial distribution is given by:
- Variance = n * p * (1 - p)
- Substituting the values:
- Variance = 3 * (1/3) * (2/3)
- Variance = 3 * (1/3) * (2/3) = 2/3
Conclusion
The variance of the number of successes when tossing a die three times, where success is defined as rolling a 2 or 5, is indeed 2/3. Thus, the correct answer is option 'B'.
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A die is tossed thrice. Success is getting 2 or 5 on a toss. What is the variance of the number of success?a)1/3b)2/3c)4/5d)35Correct answer is option 'B'. Can you explain this answer?
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