If two events A and B have nonzero probabilities and are mutually exclusive, then P(A∪B) must be a. neither b. 0 c. 1 d. cannot be determine
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A: Solution: Mutually exclusive or Disjoint events: Let A and B are two events of sample space S then…
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A: It is given that P(A) = 1/2, P(B) = 1/4, P(A ∩ B) = 1/8
Q: A and B are independent events. If Pr(A∩B)=0.18 and Pr[A]=0.3 what is Pr[B]?
A: Independent events : The event A and event B are independent if , P( A∩B ) = P( A )×P( B )
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Q: 4. The probabilities for event A and B are P(A) = 0.4 and P(B) = 0.33. Find P(A U B) if a) A and B…
A: a). Given:P(A)=0.4P(B)=0.33 The formula of probability is: P(A∪B)=P(A)+P(B)-P(A∩B) As the events are…
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Q: Suppose P(A) = 0.28 and P(B) = 0.48 and A and B are independent. Events A and B are not disjoint.…
A: Answer is mentioned below
Q: Let A, B and D be events. Show that p(A ∪ B|D) = P(A|D) + P(B|D) − ?(A ∩ B|D).
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A: Given:P(B) =0.74, P(D) =0.38 and P(B|D) = 0.74.
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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, according…
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Q: If A and B are mutually exclusive events with P(A) = .3 and P(B) = .5, then P(A∩B) =
A:
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A: Given, 3 red marbles and 4 white marbles. Total number of marbles is 7.
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Q: A and B are independent events. If Pr(A∩B)=0.4 and Pr[A]=0.5 what is Pr[B]Pr[B]?
A: It is given that, P(A)=0.5, P(A and B)=0.4.
Q: You and a group of friends are going to a five-day outdoor music festival during spring break. You…
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Q: If A and B are independent events. Then A and BC are independent.
A:
Q: If event A and event B are mutually exclusive, and P(A) = 0.5 and P(B) = 0.3, find P(A and B).
A: From given data we have : P(A)=0.5 P(B)=0.3
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A: Given: Let R be the event that the top side of the top card is red.Let B be the event that the…
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Q: Derek has a bag of marbles with 5 Blue marbles, 1 White marbles, and 1 Red marbles.Find the…
A: Given infrormation: No of blue marbles = 5 No of white marbles = 1 No of red marbles = 1 Total…
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A:
Q: Bradley has a bag of pencils with 10 orange, 2 cyan, and 5 purple pencils. Find the following…
A: Given,no.of orange pencils=10no.of cyan pencils=2no.of purple pencils=5total no.of pencils=17
Q: . P(A|C) c. P(AU B) d. P(ANC) e. P(AU C)
A: It is an important part of statistics. It is widely used.
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d. cannot be determine
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- ) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.A car can travel from Town A to Town C by using the four roads below. The probabilities of these roads being closed are P(H1), P(H2), P(H3) and P(H4). Calculate the probability that a car cannot reach Town C from Town A, knowing that the closure of the roads are independent from each other. H1 H3 TOWN A TOWN B TOWN C H2 Н4Suppose that Trendy Inc. products a style of a seasonal business suit, Sit-T-Slicker, which has a cost of $500 per unit. The demand during the season for Sit-T-Slicker is generally unknown and could be either: 200, 500, 800, 1100, and 1500 units with equal probabilities. Trendy sells the Sit-T-Slicker suit for $900 per unit during its three-month season, and for $300 per unit when sold after that time. Given the above data, what is the optimal order quantity for the Sit-T-Slicker? What is expected profit? Suppose the probabilities in part a change to 0.05, 0.25, 0.40, 0.25, 0.05 for demand levels 200, 500, 800, 1100, 1500, respectively. What is the optimal order quantity and expected profit in this case? How would better information regarding the demand for the Sit-T-Slicker suit change the data provided in this problem? How would this information affect the answers to part a? Explain.
- Your probability professor has a tabby cat who sleeps 34% of the time and seems to respond to stimuli more or less randomly. If a human pets her when she’s awake, she will request more petting 8% of the time, food 38% of the time, and a game of fetch the rest of the time. If a human pets her when she’s asleep, she will request more petting 33% of the time, food 41% of the time, and a game of fetch the rest of the time. (You can assume that the humans don’t pet her disproportionally often when she’s awake.) • If the cat requests food when petted, what is the probability that she was asleep? • If the cat requests a game of fetch when petted, what is the probability that she was not asleep?Kylie has 12 pieces of candy left in her Halloween bag. There are 8 pieces of chocolate and 4 pieces of non-chocolate. She chooses a piece of candy at random and then chooses another piece of candy, without replacement. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picks:Two pieces of chocolate No chocolate At least one piece of non-chocolate One piece of each type1. A class of 18 pupils consist of 11 girls, 4 of whom are left-handed, and 7 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act as monitors. Calculate the probabilities that the chosen pupils will consist ofa. One girl and One boyb. One girl who is left-handed and one boy who is left-handedc. Two left-handed pupils
- Please help!!! Q4. Ariana and Bella are playing a game. They each have 4 cards, which are numbered 1, 2, 3 and 4. Each shuffles her own cards and turns one over at random. If the cards show the same number, Ariana wins and Bella must pay Ariana $3. If the cards show different numbers, Bella wins and Ariana must pay Bella $1. By finding the probabilities of Ariana and Bella winning, show whether or not the game is fair.Leah is flying from Moncton to Vancouver with connection in Montreal. The proba- bility that her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Montreal is 0.95, but if the first is Practice q # 25 p.197 delayed, the probability that the luggage will make it is only 0.65. chap 7 Are the first flight leaving on time and the luggage making the connection independent events? Explain. What is the probability that Leah's luggage arrives in Vancouver with a. b. her?Write the m.g.f. of a r.v. X taking on values -4, 0 and 4 with respective probabilities 0.3, 0.4, and 0.3. 0.3 e4 +0.4 • e² + 0.3 -4z 0.3 e +0.4+ 0.3. e4z 1+0.3. e4z +0.3 · e-4z e4 0.3 ez +0.4 e² + 0.3. e4z
- where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=37 Pr[Y]=27Pr[Z]=27Pr[A|X]=45Pr[B|X]=15Pr[A|Y]=23Pr[B|Y]=13Pr[A|Z]=18Pr[B|Z]=78 Pr[(XorY)|B]=Alan has a bag of marbles with 4 blue marbles, 1 white marbles, and 2 red marbles.Find the following probabilities of Alan drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn. (Give your answer as a fraction)a) A Blue, then a red = 67Incorrect b) A red, then a white = 37Incorrect c) A Blue, then a Blue, then a Blue =
