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A, B and C are three mutually exclusive and exhaustive events such that P (A) = 2 P (B) = 3P(C). What is P (B)?
- a)6/11
- b)6/22
- c)1/6
- d)1/3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A, B and C are three mutually exclusive and exhaustive events such tha...
Given,
P(A) = 2P(B)
P(B) = x (let's assume)
P(C) = y (let's assume)
As the events are mutually exclusive and exhaustive,
P(A) + P(B) + P(C) = 1
2P(B) + P(B) + 3y = 1
3P(B) = 1 - 3y
P(B) = (1-3y)/3
We know that P(C) = y, therefore,
P(A) = 2P(B)
P(A) = 2x
Also, P(A) + P(B) + P(C) = 1
2x + x + y = 1
3x + y = 1
Substitute y = P(C) in terms of x
3x + P(C) = 1
3x + y = 1
Substitute P(C) = y in terms of P(B)
3x + (1-3P(B))/3 = 1
9x + 1 - 3P(B) = 3
9x - 3P(B) = 2
3x - P(B) = 2/3
P(B) = 3x - 2/3
Now equating the two expressions of P(B)
(1-3y)/3 = 3x - 2/3
1-3y = 9x - 2
9x - 3y = 3
3x - y = 1
Substituting this value of y in terms of x in the equation P(B) = (1-3y)/3, we get
P(B) = 6/22
Therefore, the correct answer is option B.
P(A) = 2P(B)
P(B) = x (let's assume)
P(C) = y (let's assume)
As the events are mutually exclusive and exhaustive,
P(A) + P(B) + P(C) = 1
2P(B) + P(B) + 3y = 1
3P(B) = 1 - 3y
P(B) = (1-3y)/3
We know that P(C) = y, therefore,
P(A) = 2P(B)
P(A) = 2x
Also, P(A) + P(B) + P(C) = 1
2x + x + y = 1
3x + y = 1
Substitute y = P(C) in terms of x
3x + P(C) = 1
3x + y = 1
Substitute P(C) = y in terms of P(B)
3x + (1-3P(B))/3 = 1
9x + 1 - 3P(B) = 3
9x - 3P(B) = 2
3x - P(B) = 2/3
P(B) = 3x - 2/3
Now equating the two expressions of P(B)
(1-3y)/3 = 3x - 2/3
1-3y = 9x - 2
9x - 3y = 3
3x - y = 1
Substituting this value of y in terms of x in the equation P(B) = (1-3y)/3, we get
P(B) = 6/22
Therefore, the correct answer is option B.
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Community Answer
A, B and C are three mutually exclusive and exhaustive events such tha...
A, B and C are three mutually exclusive and exhaustive events .so p(A)+p(B)+p(c)=1
let p(A)=2p(B)=3p(C)=k
k+k/2+k/3=1
k=6/11
p(B)=6/22
let p(A)=2p(B)=3p(C)=k
k+k/2+k/3=1
k=6/11
p(B)=6/22
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A, B and C are three mutually exclusive and exhaustive events such that P (A) = 2 P (B) = 3P(C). What is P (B)?a)6/11b)6/22c)1/6d)1/3Correct answer is option 'B'. Can you explain this answer?
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