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In 10 independent rollings of a biased die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. What is the probability that an even number will appear twice when the die is rolled 8 times?
  • a)
    0.0304.
  • b)
    0.1243.
  • c)
    0.2315.
  • d)
    0.1926.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In 10 independent rollings of a biased die, the probability that an ev...
Given information:
- Rolling a biased die 10 times
- Probability of getting an even number 5 times is twice the probability of getting an even number 4 times

To find:
- Probability of getting an even number twice in 8 rolls

Solution:
Let P(5) be the probability of getting an even number 5 times in 10 rolls
Let P(4) be the probability of getting an even number 4 times in 10 rolls
Then, we can write:
P(5) = 2P(4) ......(1)

Now, we need to find the probability of getting an even number twice in 8 rolls.
Let's break this down into cases:
- Case 1: even number appears twice in first 2 rolls
- Case 2: even number appears once in first 2 rolls and once in next 6 rolls
- Case 3: even number appears once in last 2 rolls and once in first 6 rolls

Probability of even number appearing twice in first 2 rolls:
P(E) = Probability of getting an even number = 1/2 (assuming the die is biased towards even numbers)
P(NE) = Probability of not getting an even number = 1 - P(E) = 1/2

So, the probability of getting an even number twice in first 2 rolls = P(E) x P(E) = (1/2) x (1/2) = 1/4

Probability of even number appearing once in first 2 rolls and once in next 6 rolls:
P(E) = Probability of getting an even number = 1/2 (assuming the die is biased towards even numbers)
P(NE) = Probability of not getting an even number = 1 - P(E) = 1/2

So, the probability of getting an even number once in first 2 rolls and once in next 6 rolls = P(E) x P(NE) x P(E) x P(NE) x P(E) x P(NE) x P(E) x P(NE) = (1/2)^4 = 1/16

Probability of even number appearing once in last 2 rolls and once in first 6 rolls:
P(E) = Probability of getting an even number = 1/2 (assuming the die is biased towards even numbers)
P(NE) = Probability of not getting an even number = 1 - P(E) = 1/2

So, the probability of getting an even number once in last 2 rolls and once in first 6 rolls = P(E) x P(NE) x P(E) x P(NE) x P(E) x P(NE) x P(E) x P(NE) = (1/2)^4 = 1/16

Adding up the probabilities from all cases, we get:
P(getting an even number twice in 8 rolls) = 1/4 + 1/16 + 1/16 = 8/64 = 1/8

Now, we can use equation (1) to find P(4):
P(5) = 2P(4)
P(4) = P(5)/2 = 1/3

Finally, we can use the binomial distribution formula to find the probability of getting an even number twice in 8
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In 10 independent rollings of a biased die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. What is the probability that an even number will appear twice when the die is rolled 8 times?a)0.0304.b)0.1243.c)0.2315.d)0.1926.Correct answer is option 'A'. Can you explain this answer?
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In 10 independent rollings of a biased die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. What is the probability that an even number will appear twice when the die is rolled 8 times?a)0.0304.b)0.1243.c)0.2315.d)0.1926.Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In 10 independent rollings of a biased die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. What is the probability that an even number will appear twice when the die is rolled 8 times?a)0.0304.b)0.1243.c)0.2315.d)0.1926.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In 10 independent rollings of a biased die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. What is the probability that an even number will appear twice when the die is rolled 8 times?a)0.0304.b)0.1243.c)0.2315.d)0.1926.Correct answer is option 'A'. Can you explain this answer?.
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