Now use the information you are given and the General Addition Rule to find the desired probability, P(smoke is detected).

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).

Recall the smoke detector example from the last activity. Here is a quick recap: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

According to the Cancer Research Institute, smoking causes 92% of all lung cancers in men. Find the probability of two randomly selected men having lung cancer caused by smoking.

Based on a recent study, the probability that someone is a smoker decreases with the person's income. If someone's family income is x thousand dollars, then the probability (expressed as a percentage) that the person smokes is approximately y = −0.31x + 40 (for 10 ≤ x ≤ 100).† Round your answers to the nearest percent.(a)Graph this line on the window [0, 100] by [0, 50].The x y-coordinate plane is given. The line enters the window at y = 40 on the positive y-axis, goes down and right, passes through the point (100, 24), and exits the window in the first quadrant. The x y-coordinate plane is given. The line enters the window at y = 40 on the positive y-axis, goes down and right, passes through the point (100, 36.9), and exits the window in the first quadrant. The x y-coordinate plane is given. The line enters the window at y = 40 on the positive y-axis, goes down and right, passes through the point (100, 9), and exits the window in the first quadrant. The x y-coordinate plane is given. The line enters the window at y = 40 on the positive y-axis, goes down and right, and exits the window at approximately x = 98 on the positive x-axis.(b)What is the probability that a person with a family income of $30,000 is a smoker? [Hint: Since x is in thousands of dollars, what x-value corresponds to $30,000?]

From a city population, the probability of selecting a male smoker is 2/5. If a male is first selected, the the probability that he is a smoker is