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A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession is
- a)(5 x 33)/45
- b)33/54
- c)33/45
- d)33/44
Correct answer is option 'D'. Can you explain this answer?
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A coin is biased so that the probability of head = 1/4. The coin is to...
Two consecutive head can appear in 4 ways remaining places goes to tail, so require probability is
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A coin is biased so that the probability of head = 1/4. The coin is to...
Probability of obtaining two heads and three tails with heads occurring in succession can be calculated using the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = (n C k) * (p^k) * (q^(n-k))
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the number of trials
- p is the probability of success in a single trial
- q is the probability of failure in a single trial (q = 1 - p)
- (n C k) represents the binomial coefficient, which is the number of ways to choose k successes from n trials
In this case, we want to find the probability of getting two heads and three tails, with heads occurring in succession. So, we have:
- n = 5 (number of trials)
- k = 2 (number of successes)
- p = 1/4 (probability of success)
- q = 1 - p = 3/4 (probability of failure)
Calculating the binomial coefficient:
(5 C 2) = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10
Calculating the probability:
P(X = 2) = 10 * ((1/4)^2) * ((3/4)^(5-2))
= 10 * (1/16) * (27/64)
= 270 / (16 * 64)
= 270 / 1024
= 33 / 128
Therefore, the probability of obtaining two heads and three tails with heads occurring in succession is 33/128.
However, none of the given options match this answer. The correct answer should be 33/128, not 33/44. It seems there might be an error in the options provided.
The binomial probability formula is given by:
P(X = k) = (n C k) * (p^k) * (q^(n-k))
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the number of trials
- p is the probability of success in a single trial
- q is the probability of failure in a single trial (q = 1 - p)
- (n C k) represents the binomial coefficient, which is the number of ways to choose k successes from n trials
In this case, we want to find the probability of getting two heads and three tails, with heads occurring in succession. So, we have:
- n = 5 (number of trials)
- k = 2 (number of successes)
- p = 1/4 (probability of success)
- q = 1 - p = 3/4 (probability of failure)
Calculating the binomial coefficient:
(5 C 2) = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10
Calculating the probability:
P(X = 2) = 10 * ((1/4)^2) * ((3/4)^(5-2))
= 10 * (1/16) * (27/64)
= 270 / (16 * 64)
= 270 / 1024
= 33 / 128
Therefore, the probability of obtaining two heads and three tails with heads occurring in succession is 33/128.
However, none of the given options match this answer. The correct answer should be 33/128, not 33/44. It seems there might be an error in the options provided.
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A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer?
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A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer?.
A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer?.
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A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession isa)(5 x 33)/45b)33/54c)33/45d)33/44Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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