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A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.?
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A coin is biased such that the probability of obtaining heads with eac...
Probability of Obtaining Heads with Biased Coin
A biased coin has a probability of obtaining heads with each toss equal to 5. We need to find the probability that the coin is tossed until the first head is obtained.
Part (a): At Least Three Times
To find the probability that the coin is tossed at least three times before obtaining the first head, we can use the geometric distribution. The probability of obtaining the first head on the k-th toss is given by:
P(X=k) = (1-p)^(k-1) * p
where p is the probability of obtaining heads on a single toss, which is equal to 5.
Therefore, the probability of obtaining the first head on or after the third toss is:
P(X>=3) = P(X=3) + P(X=4) + ...
Using the formula above, we can calculate:
P(X>=3) = (1-0.05)^2 * 0.05 + (1-0.05)^3 * 0.05 + ...
We can simplify this using the formula for an infinite geometric series:
P(X>=3) = (1-0.05)^2 * 0.05 / (1 - (1-0.05)) = 0.0476
Therefore, the probability that the coin is tossed at least three times before obtaining the first head is 0.0476.
Part (b): Fewer Than Eight Times
To find the probability that the coin is tossed fewer than eight times before obtaining the first head, we can use the same formula as above and sum up the probabilities for k=1 to k=7:
P(X<8) =="" p(x="1)" +="" p(x="2)" +="" ...="" +="" p(x="">
Using the formula for the probability of obtaining the first head on the k-th toss, we can calculate:
P(X<8) =="" 0.05="" +="" (1-0.05)="" *="" 0.05="" +="" (1-0.05)^2="" *="" 0.05="" +="" ...="" +="" (1-0.05)^6="" *="">
Again, we can simplify this using the formula for an infinite geometric series:
P(X<8) =="" 0.05="" (1-0.95^7)="">
Therefore, the probability that the coin is tossed fewer than eight times before obtaining the first head is 0.2852.
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A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.?
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A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.? 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 A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.?.
A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.? 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 A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is biased such that the probability of obtaining heads with each toss is equal to 5 -The coin is tossed until the first head is obtained. Find the probability that the coin is 11 tossed (a) at least three times (b) fewer than eight times.?.
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