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What is the probability of obtaining at least one tail when a coin is tossed five times?
- a)2/3
- b)31/32
- c)3/8
- d)1/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the probability of obtaining at least one tail when a coin is ...
‘At least one tail’ means that there can be one, two or three or four or five tails.
The only option that is not included is five heads.
The sum of all probabilities is always 1
P(at least one tail) = 1 - P(no tail)
P(no tail) = P(all heads) = P(H, H ,H, H ,H)
In any throw the probability of tail or head is ½
P(H, H ,H, H ,H) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = (1/2)5
= 1/32
P( at least one tail ) : 1 - 1/32
= 31/32 will be answer.
The only option that is not included is five heads.
The sum of all probabilities is always 1
P(at least one tail) = 1 - P(no tail)
P(no tail) = P(all heads) = P(H, H ,H, H ,H)
In any throw the probability of tail or head is ½
P(H, H ,H, H ,H) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = (1/2)5
= 1/32
P( at least one tail ) : 1 - 1/32
= 31/32 will be answer.
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
What is the probability of obtaining at least one tail when a coin is ...
To find the probability of obtaining at least one tail when a coin is tossed five times, we need to consider the complementary event, which is obtaining all heads.
- Finding the probability of obtaining all heads:
Each coin toss has two possible outcomes, heads (H) or tails (T). Since the coin is fair, the probability of obtaining heads on a single toss is 1/2.
To find the probability of obtaining all heads in five tosses, we multiply the probabilities of obtaining heads on each toss:
P(H) = 1/2
P(HHHHH) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
- Finding the probability of obtaining at least one tail:
Since the complementary event to obtaining all heads is obtaining at least one tail, we can find the probability of obtaining at least one tail by subtracting the probability of obtaining all heads from 1 (total probability).
P(at least one tail) = 1 - P(all heads) = 1 - 1/32 = 31/32
Therefore, the correct answer is option 'b) 31/32'.
- Finding the probability of obtaining all heads:
Each coin toss has two possible outcomes, heads (H) or tails (T). Since the coin is fair, the probability of obtaining heads on a single toss is 1/2.
To find the probability of obtaining all heads in five tosses, we multiply the probabilities of obtaining heads on each toss:
P(H) = 1/2
P(HHHHH) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
- Finding the probability of obtaining at least one tail:
Since the complementary event to obtaining all heads is obtaining at least one tail, we can find the probability of obtaining at least one tail by subtracting the probability of obtaining all heads from 1 (total probability).
P(at least one tail) = 1 - P(all heads) = 1 - 1/32 = 31/32
Therefore, the correct answer is option 'b) 31/32'.
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What is the probability of obtaining at least one tail when a coin is tossed five times?a)2/3b)31/32c)3/8d)1/2Correct answer is option 'B'. Can you explain this answer?
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