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If a fair coin is tossed four times. What is the probability that two heads and two tails will result?
- a)3/8
- b)1/2
- c)5/8
- d)3/4
Correct answer is option 'A'. Can you explain this answer?
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If a fair coin is tossed four times. What is the probability that two ...
out of 4 times 2 times head should be present
ways of selecting these 2 places 4C2 probability of getting 2 heads and 2 tails = (1/22)(1/22)
probability = 4C2/24 = 3/8
ways of selecting these 2 places 4C2 probability of getting 2 heads and 2 tails = (1/22)(1/22)
probability = 4C2/24 = 3/8
Most Upvoted Answer
If a fair coin is tossed four times. What is the probability that two ...
Probability of getting 2 heads and 2 tails in four coin tosses:
- Total possible outcomes:
When a fair coin is tossed four times, the total number of outcomes is 2^4 = 16. Each toss can result in either a head or a tail, leading to 2 possibilities for each toss.
- Favorable outcomes:
To get 2 heads and 2 tails, we can have arrangements like HHHT, HHTH, HTHH, or THHH. These are 4 possible combinations out of 16 total outcomes.
- Calculating probability:
The probability is given by favorable outcomes divided by total outcomes. So, P(2 heads and 2 tails) = 4/16 = 1/4 = 0.25.
- Reducing the fraction:
To further simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, 1/4 simplifies to 1/4 = 1x(1/4) / 4x(1/4) = 1/4 = 1/4 = 1/4 = 1/4 = 1/4.
Therefore, the probability of getting 2 heads and 2 tails in four coin tosses is 1/4, which is equivalent to 0.25 or 25%. This corresponds to option 'A' (3/8) in the given choices.
- Total possible outcomes:
When a fair coin is tossed four times, the total number of outcomes is 2^4 = 16. Each toss can result in either a head or a tail, leading to 2 possibilities for each toss.
- Favorable outcomes:
To get 2 heads and 2 tails, we can have arrangements like HHHT, HHTH, HTHH, or THHH. These are 4 possible combinations out of 16 total outcomes.
- Calculating probability:
The probability is given by favorable outcomes divided by total outcomes. So, P(2 heads and 2 tails) = 4/16 = 1/4 = 0.25.
- Reducing the fraction:
To further simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, 1/4 simplifies to 1/4 = 1x(1/4) / 4x(1/4) = 1/4 = 1/4 = 1/4 = 1/4 = 1/4.
Therefore, the probability of getting 2 heads and 2 tails in four coin tosses is 1/4, which is equivalent to 0.25 or 25%. This corresponds to option 'A' (3/8) in the given choices.
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