1. Tomorrow I'm going to bring a great many jelly beans to Brock. My plan is to have all 300 jars laid out in a row, and have each of the 30 students randomly select one.

Of course, it's possible two will happen to pick the same jelly bean jar, but considering the numbers I'm fairly confident the (far) more likely outcome is they'll all be unique.

What can we say about my plan?

A. With the number of students being only a tenth the number of jars, there's a 90% chance (probability of 0.9) that they'll all be unique.

B. Actually, the chances are far better than they might initially seem: using 0.1³⁰, we can say there's a0.0000000000000000000000000001% chance of overlap (meaning a 99.9999999999999999999999999999% chance of them all picking unique jars).

C. With 300 jars, and 30 students, the expectation is 30270100=81% chance of being unique. (Or approximately a 1 in 5 chance of an overlap somewhere)

D. We can say this whole plan demonstrates no understanding of statistics.

2. Suppose I have a box with several coloured balls held within. I wish to remove randomly selected balls, without replacement. Initially it contains 7 white balls, 2 red balls, and 1 purple ball. Idraw 10 balls, with 70% of them being white, 20% being red, and 10% being purple. I would like one more. What is the probability that I will then draw a white ball?

A. 0.7

B. 7

C. 7%

D. None of the above.

3. Suppose, through whatever mechanisms, I've been able to confirm that the probability, p, that a six-sided die will land displaying a 6 is p=0.1. What is the probability, q, that it will land not displaying a 6?

A. 5/6 (about 0.83)

B. 1/6 (about 0.17)

C. 9/10

D. None of the above

Suppose I have a fair coin (p_heads=p_tails=0.5).

If I flip it 10 times in a row, what's the probability of having at least one instance of heads?

A. 0.9 (9 in 10).

B. 0.1 (one in 10).

C. Still just 0.5 (or 1 in 2).

D. None of the above.