Math Help!!!

Question

3) A paper bag contains 20 slips of paper. Eight of them are blue and are numbered from 1 to 8. Twelve of them are orange and are numbered from 9 through 20. One card is picked from the bag.
a.) Find the probability of selecting an orange card or a multiple of 4.
b.) Find the probability of selecting a blue card or a card with the number 18 on it.

Answer 1

You can use the following formula:

 

P(A or B) = P(A) + P(B) - P(A and B)

 

a) Let event A be that the card is orange.  Out of 20 cards, 12 are orange. P(A) = 12/20.

Let event B be that the card is a multiple of 4.  The cards number from 1 to 20, so 20/4 = 5 are the number of cards which are multiples of 4.  P(B) is then 5/20.

 

event (A and B) consists of cards which are orange and multiples of 4.  This event consists of three orange cards numbered 12,16, and 20. So P(A and B) is 3/20.

 

Throwing it all into the formula, we have 12/20 + 5/20 - 3/20 = 14/20.

 

b) Let event A be that the card is blue, and event B be that the card is numbered 18.

P(A) = 8/20

P(B) = 1/20

 

Use P(A or B) = P(A) + P(B) - P(A and B).  Hint:  There are no blue cards numbered 18.