Let C1, C2, C3 be independent events with probabilities 1/2, 1/3, 1/4 respectivel Q.3. Compute P(CUC2ŪC3).
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- If A and B are two mutually exclusive events with P(A)= 0.5 and P(B)=0.4, find the following probabilities: a) P(A \textrm{ and } B) = 0.5 b) P(A \textrm{ or } B) = c) P( \textrm{not }A ) = d) P( \textrm{not }B ) = 0.4 e) P( \textrm{not }(A \textrm{ or } B)) = 0.4 f) P( A \textrm{ and } (\textrm{not }B) ) =A new box of 40 candles contains 3 defective candles. Find the probability of selecting 3 candles and 13. all 3 candles are defective calo bsb mot hY 14. none are defective 15. At least one is defectiveThe probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes him) is .75. a.) Write down the 3 pieces of information given in terms of probabilities involving event A (Taylor Swift is Austin’s favorite music artist) and event B (Austin will go to a Taylor Swift concert). b.) Summarize the above information using a probability table. c.) Find the probability that Taylor Swift is Austin’s favorite music artist or Austin will go to a Taylor Swift concert.
- Suppose, in an airport, there are three runways. In the ideal situation, the probabilities, 2/9, 1/6, and 11/18 represent the likelihood that individual runways 1, 2 and3 respectively are accessed by a randomly arriving commercial jet. If 6 airplanes are arriving at the airport then what is the probability that there are 2, 1, and 3 airplanes are accessed by runway 1, runway 2, and runway respectively.Suppose there are 6 red balls and 4 white balls in a urn.(1) event A={First draw is a white ball}, what is P(A), probability of A?(2) Now assume we do picking balls one by one without replacement. event B={Second draw is a white ball}, what is P(B), probability of B? (3) Are A and B independent? Justify your answer. please explain and do all the steps fully!2. A fair six-sided die is tossed twice. What is the probability that a five will occur at least once?
- 6. Let A, B, C be three events with P(A) = P(B) = P(C) = 1, P(AC) = 1, P(AB) = P(BC) = 0, determine the probability of the event that at least one of A, B, C occurs.A cook is preparing fruit jam for the festival next week. She has bought 30 apples from the farmer's market and unknown to the cook, 8 of these apples are not fresh. She will randomly select 10 apples to prepare the jam. What is the probability that she will use at least 3 of the apples that are not fresh for preparing the jam?Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbsof which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3 contains 3 defective and 4 functional bulbs. A box is selected at random and a bulbdrawn from it at random is found to be defective. Find the probability that the boxselected was Box 2. [9 Marks]
