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Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
- a)1/16
- b)1/8
- c)7/8
- d)15/16
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Four fair coins are tossed simultaneously. The probability that at lea...
probability of getting all heads = 1/16
probability of getting all tails = 1/16
probability of getting at least one head and one tail = 1 - 1/16 - 1/16 = 7/8
probability of getting all tails = 1/16
probability of getting at least one head and one tail = 1 - 1/16 - 1/16 = 7/8
Most Upvoted Answer
Four fair coins are tossed simultaneously. The probability that at lea...
Solution:
To find the probability of at least one head and one tail turning up when four fair coins are tossed simultaneously, we can use the concept of complementary probability.
Complementary Probability:
The complementary probability of an event is the probability that the event does not occur. It is denoted by P(A').
We can find the probability of at least one head and one tail turning up as follows:
Step 1: Find the probability of getting all heads or all tails when four fair coins are tossed simultaneously.
The probability of getting all heads or all tails is:
P(all heads or all tails) = P(all heads) + P(all tails)
= (1/2)^4 + (1/2)^4
= 1/8 + 1/8
= 1/4
Step 2: Find the complementary probability of getting all heads or all tails.
The complementary probability of getting all heads or all tails is the probability that at least one head and one tail turn up.
P(at least one head and one tail) = 1 - P(all heads or all tails)
= 1 - 1/4
= 3/4
Therefore, the probability that at least one head and one tail turn up when four fair coins are tossed simultaneously is 3/4 or 0.75.
Answer: Option C (7/8)
To find the probability of at least one head and one tail turning up when four fair coins are tossed simultaneously, we can use the concept of complementary probability.
Complementary Probability:
The complementary probability of an event is the probability that the event does not occur. It is denoted by P(A').
We can find the probability of at least one head and one tail turning up as follows:
Step 1: Find the probability of getting all heads or all tails when four fair coins are tossed simultaneously.
The probability of getting all heads or all tails is:
P(all heads or all tails) = P(all heads) + P(all tails)
= (1/2)^4 + (1/2)^4
= 1/8 + 1/8
= 1/4
Step 2: Find the complementary probability of getting all heads or all tails.
The complementary probability of getting all heads or all tails is the probability that at least one head and one tail turn up.
P(at least one head and one tail) = 1 - P(all heads or all tails)
= 1 - 1/4
= 3/4
Therefore, the probability that at least one head and one tail turn up when four fair coins are tossed simultaneously is 3/4 or 0.75.
Answer: Option C (7/8)
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Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up isa)1/16b)1/8c)7/8d)15/16Correct answer is option 'C'. Can you explain this answer?
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