Is this problem missing something? Who is the "they"? go back to complore and recopy this. Thanks in advance.

are the variables A, B, and C distances? you said probabilit yof hitting a target BY..

harsh.champ wrote:In a shooting competition, the probability of hitting the target by A is 2/5, by B is 2/3 and by C is 3/5. If all of them fire independently at the same target, calculate the probability that only one of them will hit the target.

A.1/2
B.1/3
C.1/4
D.1/5
E.1/6

3 cases A hits B C misses, prob = 2/5*1/3*2/5 = 4/75
B hits A C misses, prob = 3/5*2/3*2/5 = 12/75
C hits A B misses = 3/5*1/3*3/5 = 9/75

total = 25/75 = 1/3

money9111 wrote:are the variables A, B, and C distances? you said probabilit yof hitting a target BY..

Its clearly written probability of hitting the target by A is 2/5, by B is 2/3 and by C is 3/5.. how can "by" refer a distance. A, B and C are not variables but they are referring to a person(either male or female or ...)

harsh.champ wrote:In a shooting competition, the probability of hitting the target by A is 2/5, by B is 2/3 and by C is 3/5. If all of them fire independently at the same target, calculate the probability that only one of them will hit the target.

A.1/2
B.1/3
C.1/4
D.1/5
E.1/6

P(A) = 2/5, P(B) =2/3, P(C)= 3/5 -----> P(A') = 3/5, P(B') =1/3, P(C')= 2/5
P(only one hit target) = P(A')P(B')P(C)+P(A')P(B)P(C')+P(A)P(B')P(C') = 3/5 x 1/3 x 3/5 + 3/5 x 2/3 x 2/5 + 2/5 x 1/3 x 2/5 = 25/75 =1[spoiler]/3 Ans B[/spoiler]

@ shashank.ism - i'm going to disagree with you here... by saying that the probability of hitting the target BY A is 2/5... could and in my opinion does in fact mean a distance.

i think you... well Harsh.Champ meant to type "...hitting the Target A is 2/5" and not "...hitting the target by A is 2/5" do you see the difference?

money9111 wrote:@ shashank.ism - i'm going to disagree with you here... by saying that the probability of hitting the target BY A is 2/5... could and in my opinion does in fact mean a distance.

i think you... well Harsh.Champ meant to type "...hitting the Target A is 2/5" and not "...hitting the target by A is 2/5" do you see the difference?

Money, substitute A for a person's name and I think you'll get where shashank is coming from.

If A=Money9111, the original stem reads,
"In a shooting competition, the probability of hitting the target by Money9111 is 2/5..."

It could be rewritten so that "In a shooting competition, the probability of A (Money9111) hitting the target is 2/5" is less ambiguous, but A musn't be a distance I do not think.

osirus0830 wrote:Is this problem missing something? Who is the "they"? go back to complore and recopy this. Thanks in advance.

Hey osirus,
I couldn't get ur doubt-"They".Are you finding any problem with the wording of the problem?
Anyways this problem is not from complore. It is a very common type of probability problem,I guess and can be found in numerous resources.I don't know if complore is one of them.Anyways,do let me know your doubt about the question.

money9111 wrote:are the variables A, B, and C distances? you said probabilit yof hitting a target BY..

No,A,B,C are not distances.They are 3 different persons.[You can change A,B,C to Tom,Dick and Harry to get a better clarity of the question]Probability of hitting the target by A means "if the 1st person hits the target" not "the distance y which he/she hits it".

harsh.champ wrote:In a shooting competition, the probability of hitting the target by A is 2/5, by B is 2/3 and by C is 3/5. If all of them fire independently at the same target, calculate the probability that only one of them will hit the target.

A.1/2
B.1/3
C.1/4
D.1/5
E.1/6

Well guys ,I would just post the solution now so that nobody has any other doubts.
I guess if not specified otherwise,we take the events to be mutually exclusive.
Soln:- P(only one of them hit the target ) = P(A hits,B misses,C misses) + P(B hits,A misses,C misses) +
P(C hits,B misses,A misses)
=(2/5 x 1/3 x 2/5) + (2/3 x 3/5 x 2/5) + (3/5 x 3/5 x 1/3)
=[spoiler]25/75 = 1/3 B[/spoiler]

I guess the soln. is clear now.

BSDesis wrote:

money9111 wrote:@ shashank.ism - i'm going to disagree with you here... by saying that the probability of hitting the target BY A is 2/5... could and in my opinion does in fact mean a distance.

i think you... well Harsh.Champ meant to type "...hitting the Target A is 2/5" and not "...hitting the target by A is 2/5" do you see the difference?

Money, substitute A for a person's name and I think you'll get where shashank is coming from.

If A=Money9111, the original stem reads,
"In a shooting competition, the probability of hitting the target by Money9111 is 2/5..."

It could be rewritten so that "In a shooting competition, the probability of A (Money9111) hitting the target is 2/5" is less ambiguous, but A musn't be a distance I do not think.

Thanks BSDesis to clear the concept by giving some real life examples..
I meant the same that A,B, C are the persons Just replace A,B,C by any persons name and you will feel that it is actually representing a person..