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Three fair coins are tossed simultaneously. What is the probability of getting at least one head and one tail?
- a)3/4
- b)3/8
- c)7/8
- d)5/8
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three fair coins are tossed simultaneously. What is the probability of...
Formula Used:
Probability = (Number of successful outcomes/Total number of outcomes)
P(E) = (nE)/(nS), where nE = Number of events and nS = Number of sample space
Calculation:
When three coins are tossed, total possible outcomes = 8
S = {HHH, HHT, HTT, THH, TTH, THT, HTH}
Favourable cases = {HHT, HTT, THH, TTH, THT, HTH}
Here, H = Head, T = Tail
P(getting at least one head, one tail) = 6/8 = 3/4
∴ The probability is 3/4.
Most Upvoted Answer
Three fair coins are tossed simultaneously. What is the probability of...
Formula Used:
Probability = (Number of successful outcomes/Total number of outcomes)
P(E) = (nE)/(nS), where nE = Number of events and nS = Number of sample space
Calculation:
When three coins are tossed, total possible outcomes = 8
S = {HHH, HHT, HTT, THH, TTH, THT, HTH}
Favourable cases = {HHT, HTT, THH, TTH, THT, HTH}
Here, H = Head, T = Tail
P(getting at least one head, one tail) = 6/8 = 3/4
∴ The probability is 3/4.
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Community Answer
Three fair coins are tossed simultaneously. What is the probability of...
Question Analysis:
We are given three fair coins, and we need to find the probability of getting at least one head and one tail when all three coins are tossed simultaneously.
Approach:
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have at least one head and one tail, we can have the following favorable outcomes:
- HHT (Head, Head, Tail)
- HTH (Head, Tail, Head)
- THH (Tail, Head, Head)
- TTH (Tail, Tail, Head)
- THT (Tail, Head, Tail)
- HTT (Head, Tail, Tail)
Therefore, there are six favorable outcomes.
Total Outcomes:
The total number of outcomes when three coins are tossed simultaneously is given by 2^3 = 8. (Each coin can have two possible outcomes: head or tail)
Probability Calculation:
The probability of an event is given by the ratio of favorable outcomes to total outcomes. Therefore, the probability of getting at least one head and one tail when three coins are tossed simultaneously is:
= (Number of favorable outcomes) / (Total number of outcomes)
= 6/8
= 3/4
Final Answer:
The probability of getting at least one head and one tail when three coins are tossed simultaneously is 3/4, which corresponds to option A.
We are given three fair coins, and we need to find the probability of getting at least one head and one tail when all three coins are tossed simultaneously.
Approach:
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have at least one head and one tail, we can have the following favorable outcomes:
- HHT (Head, Head, Tail)
- HTH (Head, Tail, Head)
- THH (Tail, Head, Head)
- TTH (Tail, Tail, Head)
- THT (Tail, Head, Tail)
- HTT (Head, Tail, Tail)
Therefore, there are six favorable outcomes.
Total Outcomes:
The total number of outcomes when three coins are tossed simultaneously is given by 2^3 = 8. (Each coin can have two possible outcomes: head or tail)
Probability Calculation:
The probability of an event is given by the ratio of favorable outcomes to total outcomes. Therefore, the probability of getting at least one head and one tail when three coins are tossed simultaneously is:
= (Number of favorable outcomes) / (Total number of outcomes)
= 6/8
= 3/4
Final Answer:
The probability of getting at least one head and one tail when three coins are tossed simultaneously is 3/4, which corresponds to option A.
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Three fair coins are tossed simultaneously. What is the probability of getting at least one head and one tail?a)3/4b)3/8c)7/8d)5/8Correct answer is option 'A'. Can you explain this answer?
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