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Two coins are tossed simultaneously. What is the probability that the second coin would show a tail given that the first coin has shown a head?
- a)0.25
- b)0.50
- c)0.75
- d)0.125
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two coins are tossed simultaneously. What is the probability that the ...
Given:
Two coins are tossed simultaneously.
First coin shows a head.
To find:
Probability that the second coin would show a tail.
Solution:
There are four possible outcomes when two coins are tossed simultaneously:
HH, HT, TH, TT
Out of these four outcomes, only one outcome satisfies the given condition:
HT
So, the probability that the second coin would show a tail given that the first coin has shown a head is 1/2 or 0.50.
Therefore, the correct answer is option A.
Explanation:
We can also solve this problem using conditional probability formula:
P(A | B) = P(A and B) / P(B)
where,
P(A | B) is the conditional probability of event A given that event B has occurred.
P(A and B) is the probability of both events A and B occurring together.
P(B) is the probability of event B occurring.
In this problem, event A is "second coin shows a tail" and event B is "first coin shows a head".
P(B) = probability of first coin showing a head = 1/2 (since there are two equally likely outcomes - head or tail)
P(A and B) = probability of both events A and B occurring together = 1/4 (since there are four equally likely outcomes and only one outcome satisfies both events - HT)
Therefore, the conditional probability of event A given that event B has occurred is:
P(A | B) = P(A and B) / P(B) = (1/4) / (1/2) = 1/2 or 0.50
Hence, the probability that the second coin would show a tail given that the first coin has shown a head is 0.50 or 50%.
Two coins are tossed simultaneously.
First coin shows a head.
To find:
Probability that the second coin would show a tail.
Solution:
There are four possible outcomes when two coins are tossed simultaneously:
HH, HT, TH, TT
Out of these four outcomes, only one outcome satisfies the given condition:
HT
So, the probability that the second coin would show a tail given that the first coin has shown a head is 1/2 or 0.50.
Therefore, the correct answer is option A.
Explanation:
We can also solve this problem using conditional probability formula:
P(A | B) = P(A and B) / P(B)
where,
P(A | B) is the conditional probability of event A given that event B has occurred.
P(A and B) is the probability of both events A and B occurring together.
P(B) is the probability of event B occurring.
In this problem, event A is "second coin shows a tail" and event B is "first coin shows a head".
P(B) = probability of first coin showing a head = 1/2 (since there are two equally likely outcomes - head or tail)
P(A and B) = probability of both events A and B occurring together = 1/4 (since there are four equally likely outcomes and only one outcome satisfies both events - HT)
Therefore, the conditional probability of event A given that event B has occurred is:
P(A | B) = P(A and B) / P(B) = (1/4) / (1/2) = 1/2 or 0.50
Hence, the probability that the second coin would show a tail given that the first coin has shown a head is 0.50 or 50%.
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Community Answer
Two coins are tossed simultaneously. What is the probability that the ...
The sample space for two coins is {HH,HT,TH,TT}, n(S)=4
Favourable outcomes for the first coin head and second coin showing tail are HT, n(E)=1
Hence, the probability that the second coin would show a tail given that the first coin has shown a head is n(E)/n(S) = 1/4 = 0.25
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Two coins are tossed simultaneously. What is the probability that the second coin would show a tail given that the first coin has shown a head?a)0.25b)0.50c)0.75d)0.125Correct answer is option 'A'. Can you explain this answer?
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