Engineering Board Exam Reviewer · Mutually Exclusive and Independent Events · medium

Events A and B are independent, with P(A)=0.4 and P(A B)=0.7. Find P(B).

  1. 0.5
  2. 0.3
  3. 0.7
  4. 0.75

Answer

A. 0.5

Solution

0.7=0.4+P(B)-0.4P(B) 0.3=0.6P(B) P(B)=0.5.

More Mutually Exclusive and Independent Events questions

  1. A system has 3 components in series, each working independently with probability 0.95. Find the probability that the system works.
  2. Two machines operate independently. Machine 1 works with probability 0.9 and machine 2 with probability 0.8. Find the probability that at…
  3. Two fair dice are rolled. Let A be the event that the sum is 8 and B the event that the first die shows 4. Are A and B independent?
  4. Events A and B are independent with P(A)=0.6 and P(B)=0.5. Find P(A B).
  5. Events A and B are independent with P(A)=0.7 and P(B)=0.2. Find P(A B).
  6. Events A and B are mutually exclusive with P(A)=0.5 and P(B)=0.3. Find P(A B).
  7. A single card is drawn from a deck. What is the probability that it is a heart or a spade? (These are mutually exclusive events.)
  8. A bag has 5 red and 7 blue balls. A ball is drawn, replaced, then another is drawn. What is the probability that both are red? (These are…
  9. The probability that event A occurs is 0.4 and event B occurs is 0.5. If A and B are independent, find the probability that both occur.
  10. The probability of rain tomorrow is 0.3 and the probability of rain the day after is 0.4, and the two events are independent. Find the…

All Mutually Exclusive and Independent Events questions