See attached file.
1. Find the following probabilities:
(A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3 and P(A or B) = 0.40, find P(B).
(B) Events A and B are defined on a common sample space. If P(A) = 0.50, P(B) = 0.50, and P(A or B) = 0.60, find P(A and B)
2. A bag of jelly belly candies contains the following colored jelly beans: red (6), blue (2), orange (5), brown (21), green (10), and yellow (6). Construct the probability distribution for x.
x 1 2 3
P(x) 0.2 0.6 0.2
4. Classify the following as discrete or continuous random variables.
(A) The weight of a school bus containing 22 football players
(B) The number of times required for a modem to dial an internet provider before connecting
(C) A pair of dice is rolled, and the sum to appear on the dice is recorded
(D) The blades of grass on a front lawn
5. In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 15 patients using the drug is selected. Find the probability that:
(A) exactly three will have this mild side effect
(B) at least two will have this mild side effect.
6. X has a normal distribution with a mean of 75.0 and a standard deviation of 3.5. Find the following probabilities:
(A) P(x < 73.0)
(B) P(72.0 < x < 78.0)