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1. Teesha is in the French club. There are 31 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that Teesha will be picked as a guide? Hint: Teesha must be picked first or second.

Teesa can be  paired with 30 other students...so...she can appear in 30 possible sets   

The total possible sets = C(31, 2)  = 465

So...the probabilty  that she is picked is   30 / 465  = 2/31

2. What is the probability of rolling a sum of 5 on at least one of two rolls of a pair of number cubes?

A. 1/81  B. 25/1296  C. 2/9  D. 17/81

This equals to   

1  - probability of no 5s  on either roll  

There 4 ways to roll a 5 on one roll....and there are 36 possible outcomes...so 32 of them are not a sum of 5

So...the probability is :

1 - (32/36)(32/36)  =

1 - (32/36)^2  =

17 / 81 

3. Suppose you flip a coin and roll a number cube. What is the probability of having tails come up on the coin and an even number on the number cube?

Possibiily of  tails  = 1/2    = A

Possibility of even number  = 1/2  = B

So 

Prob ( A  and B )  = 

(1/2) (1/2)  =  1/4

4. Your English teacher has decided to randomly assign poems for the class to read. The syllabus includes 2 poems by Shakespeare, 5 poems by Coleridge, 4 poems by Tennyson, and 3 poems by Lord Byron. What is the probability that you will be assigned a poem by Coleridge and then a poem by Lord Byron?

We have  14 poems

Prob of Coleridge  = 5/14  =   A

After this....we only have 13 poems from which to choose

Prob of Byron = 3/13

Prob (A and B) =

5/14 * 3/13  =

15 / 182  

P.S.  -  hope you get to feeling better  !!!