D—the dining room alarm is set off by smoke in the kitchenB—the bedroom alarm is set off by smoke in the kitchenP(D) = 0.95P(B) = 0.40D and B are independent → P(D and B) = 0.38Complete the table below. Start with the information that is given and go from there.Learn By DoingComplete the following table: What is the probability that goes in each cell?B not B TotalD      not D      Total

A homeowner has two smoke detector alarms installed, one in the dining room (adjacent to the kitchen) and one in an upstairs bedroom (above the kitchen). If cooking produces smoke in the kitchen, the probability of setting off the dining room alarm (D) is .95. The probability of setting off the bedroom alarm (B) is .40. The two alarms detect smoke independently of each other. If there is smoke in the kitchen, what is the probability that the smoke will be detected and will set off an alarm?Let's first understand what probability we need to find: The smoke from the fire is detected if it sets off the dining room alarm (D) or the bedroom alarm (B) or both, and therefore P(smoke is detected) = P(D or B), which is the probability we need to find. To that end, we are given a few pieces of information. Let's summarize them:To that end, we are given a few pieces of information. Let's summarize them:* P(D) = .95* P(B) = .4* Unlike the previous examples, in which P(A and B) was simply given, here we have a different piece of information: "The two alarms detect smoke independently of each other." In other words, instead of being given P(D and B), we are given the fact that D and B are independent.Explain why we have enough information to find P(D and B); then find P(D and B).

A and B are independent events. P(A) = 0.50 and P(B) = 0.20.What is P(A and B)?A.0B.0.70C.0.01D.0.10

A and B are independent events.P(A) = 0.50P(B) = 0.20What is P(A|B)?A.0.20B.Not enough informationC.0.50D.0.10SUBMITarrow_backPREVIOUS

P(A) = 0.20P(B) = 0.25P(A and B) = 0.10What is P(B|A)?A.0.25B.0.05C.0.50D.0.40SUBMITarrow_backPREVIOUS

A and B are independent events.P(A) = 0.30P(B) = 0.60What is P(A|B)?A.0.18B.0.60C.Not enough informationD.0.30