Suppose we have two bowls full of candies | Complete Solution

1. Suppose we have two bowls full of candies. Each bowl contains four different flavours of candy - grape (which are purple), lemon (which are yellow), cherry (which are red) and raspberry (which are also red).

(a) We will randomly select one candy from each bowl. The outcome of interest is the flavour of each of the two candies. Write out the complete sample space of outcomes.
(b)Suppose instead that we randomly select one candy from each bowl, and the outcome of interest is the colour of each of the two selected candies. Write out the complete sample space of outcomes.


2.*Give all probabilities to four decimal places.

Bowl #1 contains 2 grape candies, 5 lemon candies, 8 cherry candies and 5 raspberry candies.

Bowl #2 contains 8 grape candies, 7 lemon candies, 4 cherry candies and 1 raspberry candies.

(c) What is the probability that the two selected candies are the same flavour?

(d) What is the probability that the two selected candies are different colours?

(e) What is the probability that the first selected candy is lemon or that the second selected candy is cherry?

(f) Let X be the number of grape candies that are selected. Find the probability distribution of X by filling in the table below:




X 0 1 2
P(X = x)

Question 2.
Percentage grades in a large chemistry class follow a normal distribution with mean 67 and standard deviation 8.

(a) What proportion of students in the class receive a grade lower than 56.5?

(b) What proportion of students in the class receive a grade higher than 71.6?

(c) What proportion of students in the class receive a grade between 60.2 and 72.2?

(d) Students with the lowest 9% of grades will receive an F in the course. What is the minimum grade required to pass the course?

(e) According to the 68-95-99.7 Rule, approximately 95% of students in the class receive grades between and

(f) Percentage grades in a large biology class follow a normal distribution with standard deviation 8.3. It is known that 20% of students receive grades higher than 75.97. What is the mean grade in the class?

(g) Percentage grades in a large physics class follow a normal distribution with mean 60. It is known that 3% of students receive grades less than 41.2. What is the standard deviation of grades in the class?

(h) One student received a grade of 75.8 in chemistry, a grade of 78.96 in biology, and a grade of 73 in physics. In which class did the student to the best, relative to other students in the class?

Chemistry

Physics

Biology

The student did equally well in all three classes relative to other students.