For the next three (03) items that follow : Let A, B, C and D be mutually exclusive and exhaustive events such that \(\dfrac{P(A)}{6} = \dfrac{P(B)}{3} = \dfrac{P(C)}{4} = \dfrac{P(D)}{2}\).
What is \(\dfrac{P(A)+2P(B)}{3P(C)+P(D)}\) equal to?
\(\dfrac{6}{7}\)
Let \(\dfrac{P(A)}{6}=\dfrac{P(B)}{3}=\dfrac{P(C)}{4}=\dfrac{P(D)}{2}=k\), so \(P(A)=6k, P(B)=3k, P(C)=4k, P(D)=2k\). Then \(\dfrac{P(A)+2P(B)}{3P(C)+P(D)} = \dfrac{6k+6k}{12k+2k} = \dfrac{12k}{14k} = \dfrac{6}{7}\).
Similar Questions
Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
Consider the following relations for two events E and F:
1. P(E ∩ F) ≥ P(E) + P(F) - 1
2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F)
3. P(E ∪ F) ≤ P(E) + P(F)
Which of the above relations is/are correct?
Two similar boxes B i(i = 1, 2) contain (i + 1) red and (5 – i – 1) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours?
If \(P(A\cap B) = 1/2\) and \(P(\overline{A}\cap\overline{B}) = 1/2\), and \(2P(A) = P(B) = k\), then what is the value of \(k\)?
Consider the following statements for three events A, B and C:
I. \(P(A\cap B\cap C) \le P(A)+P(B)+P(C)-2\)
II. \(P(A\cup B\cup C) \ge P(A)+P(B)+P(C)\)
Which of the statements given above is/are correct?
Important Questions from Addition Theorem of Events
Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
Consider the following relations for two events E and F:
1. P(E ∩ F) ≥ P(E) + P(F) - 1
2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F)
3. P(E ∪ F) ≤ P(E) + P(F)
Which of the above relations is/are correct?
Two similar boxes B i(i = 1, 2) contain (i + 1) red and (5 – i – 1) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours?
If \(P(A\cap B) = 1/2\) and \(P(\overline{A}\cap\overline{B}) = 1/2\), and \(2P(A) = P(B) = k\), then what is the value of \(k\)?
Consider the following statements for three events A, B and C:
I. \(P(A\cap B\cap C) \le P(A)+P(B)+P(C)-2\)
II. \(P(A\cup B\cup C) \ge P(A)+P(B)+P(C)\)
Which of the statements given above is/are correct?
