The following questions cover basic probability concepts, the complement rule, union/intersection, independence, conditional probability, and counting rules.

Items are selected out of a bin, one by one, until one is deformed. Let the random variable X = the number of items selected until a deformed item is found.  Does the random variable X follow a binomial distribution? 

A box of 180 fair six-sided dice is dropped, and they are scattered all over the floor. How many do you expect to land so that the number “2” is showing on the top side? (Hint: If the dice are fair, then the probability of success, p, is equal to….._). 

If P(A) = 0.35, what is P(not A)?

Using the function \(f(x) = x^2 + x\) for each step, evaluate and simplify the following expressions (where \(h \neq 0\)). Make sure to combine like terms and simplify when possible.\(f(1+h) =\) [fh1]\(f(1+h) – f(1) =\) [fh2]\(\displaystyle \lim_{h \to 0} \frac{f(1+h) – f(1)}{h} =\) [fh3]Equation of the tangent line to \(f(x)\) at the point \((1, 2)\): [fh4]

(Q5.4.c)  The data given below represents the number of traffic fatalities by seat location and gender. Female Male Total Driver 32,955 11,732 44,687 Passenger 6,390 6,243 12,633 Total 39,345 17,975 57,320 Determine P(Male) and P( Male | Driver ).  Show how you found each answer. Then say if the events “Male” and “Driver” are independent and explain how you know.

The following questions cover discrete and continuous probability distributions, the binomial distribution, the normal distribution, the Central Limit Theorem, and the t-distribution.

The notation P(A|B) represents:

Using the angle \(\theta\) of the right triangle given below, find \(\sin(\theta)\). 

The mean gestation time of a litter of puppies is approximately bell-shaped with a mean of 60 days and a standard deviation of 6 days. Using technology, what percent of gestation times are between 50 and 55 days? Round your answer to the nearest tenth of a percent.  Answer: [1]%