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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?
Verified 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
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 ...
P(E1)=1 that it is head
p(E2)=0.50 probability of tails
p(E2/E1)=0.50
p(E2)=0.50 probability of tails
p(E2/E1)=0.50
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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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