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How many tosses of a coin are needed so that the probability of getting at least one head is 0.875?
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How many tosses of a coin are needed so that the probability of gettin...
Probability of getting at least one head in coin toss
In order to find out how many coin tosses are needed to get at least one head with a probability of 0.875, we need to understand the concept of probability and its calculation. Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Calculation of probability
The probability of getting at least one head in a coin toss can be calculated using the formula:
P(at least one head) = 1 - P(no head)
Where P(no head) is the probability of getting no head in a coin toss.
The probability of getting no head in a single coin toss is:
P(no head) = 1/2
Therefore, the probability of getting at least one head in a single coin toss is:
P(at least one head) = 1 - P(no head) = 1 - 1/2 = 1/2
Calculation of number of coin tosses
In order to find out how many coin tosses are needed to get at least one head with a probability of 0.875, we can use the following formula:
P(at least one head) = 1 - (1/2)^n
Where n is the number of coin tosses.
Substituting the given probability value, we get:
0.875 = 1 - (1/2)^n
Solving for n, we get:
n = log(0.125) / log(0.5) = 3
Therefore, the number of coin tosses needed to get at least one head with a probability of 0.875 is 3.
Conclusion
In conclusion, we have seen that the probability of getting at least one head in a single coin toss is 1/2. Using this probability, we have calculated the number of coin tosses needed to get at least one head with a probability of 0.875 to be 3.
Community Answer
How many tosses of a coin are needed so that the probability of gettin...
In the tossing of three head
Sample space={ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }
n(s) =8
Event A= Getting atleast one head
A={HHH, HHT, HTH, HTT, THH, THT, TTH}
n(a) = 7
n(A)
p(A)= ——— = 7/8=0.875
n(s)
Sample space={ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }
n(s) =8
Event A= Getting atleast one head
A={HHH, HHT, HTH, HTT, THH, THT, TTH}
n(a) = 7
n(A)
p(A)= ——— = 7/8=0.875
n(s)
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How many tosses of a coin are needed so that the probability of getting at least one head is 0.875?
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How many tosses of a coin are needed so that the probability of getting at least one head is 0.875? 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 How many tosses of a coin are needed so that the probability of getting at least one head is 0.875? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many tosses of a coin are needed so that the probability of getting at least one head is 0.875?.
How many tosses of a coin are needed so that the probability of getting at least one head is 0.875? 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 How many tosses of a coin are needed so that the probability of getting at least one head is 0.875? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many tosses of a coin are needed so that the probability of getting at least one head is 0.875?.
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