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A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?
- a)1/4
- b)3/8
- c)1/2
- d)3/4
Correct answer is option 'A'. Can you explain this answer?
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To find the probability of getting heads exactly 3 times when a coin is tossed 4 times, we can use the concept of binomial probability.
The binomial probability formula is given by:
P(x) = (nCx) * p^x * q^(n-x)
Where:
P(x) is the probability of getting x successes,
n is the number of trials (coin tosses),
x is the number of successful outcomes (getting heads),
p is the probability of success on a single trial (getting heads),
q is the probability of failure on a single trial (getting tails), and
(nCx) represents the binomial coefficient, which can be calculated as n! / (x! * (n-x)!)
In this case, we want to find the probability of getting heads exactly 3 times, so x = 3, n = 4, p = 1/2 (since the probability of getting heads is 1/2 for a fair coin), and q = 1/2 (since the probability of getting tails is also 1/2 for a fair coin).
Now we can substitute these values into the binomial probability formula:
P(3) = (4C3) * (1/2)^3 * (1/2)^(4-3)
P(3) = (4C3) * (1/2)^3 * (1/2)^1
P(3) = (4! / (3! * (4-3)!)) * (1/2)^3 * (1/2)^1
P(3) = (4! / (3! * 1!)) * (1/8) * (1/2)
P(3) = (4 * 1) * (1/8) * (1/2)
P(3) = 4/16
P(3) = 1/4
Therefore, the probability of getting heads exactly 3 times when a coin is tossed 4 times is 1/4, which corresponds to option A.
The binomial probability formula is given by:
P(x) = (nCx) * p^x * q^(n-x)
Where:
P(x) is the probability of getting x successes,
n is the number of trials (coin tosses),
x is the number of successful outcomes (getting heads),
p is the probability of success on a single trial (getting heads),
q is the probability of failure on a single trial (getting tails), and
(nCx) represents the binomial coefficient, which can be calculated as n! / (x! * (n-x)!)
In this case, we want to find the probability of getting heads exactly 3 times, so x = 3, n = 4, p = 1/2 (since the probability of getting heads is 1/2 for a fair coin), and q = 1/2 (since the probability of getting tails is also 1/2 for a fair coin).
Now we can substitute these values into the binomial probability formula:
P(3) = (4C3) * (1/2)^3 * (1/2)^(4-3)
P(3) = (4C3) * (1/2)^3 * (1/2)^1
P(3) = (4! / (3! * (4-3)!)) * (1/2)^3 * (1/2)^1
P(3) = (4! / (3! * 1!)) * (1/8) * (1/2)
P(3) = (4 * 1) * (1/8) * (1/2)
P(3) = 4/16
P(3) = 1/4
Therefore, the probability of getting heads exactly 3 times when a coin is tossed 4 times is 1/4, which corresponds to option A.
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