Solutions to Practice Problems for  the Lander Math Contest
Module 1, Solutions (1-3):

1)     a) The probability of the event is P(ace of diamonds) + P
(queen of clubs) + P(king)=1/52+1/52+4/52=6/52=3/26.
(Note: we can sum the probabilities because there is no
overlap.)

b) Notice that the total number of outcomes when rolling two
dice is 36 (6x6). Number 9 is rolled in four different ways: (1)
if the first die is 3, and the second die is 6, or (2) vice versa 6
and 3. Also, (3) first die is 4, second is 5 and (4) vice versa.
Since all outcomes are equally probable, the probability of
rolling a 9 is 4/36 =1/9. (Note: we can sum the probabilities
because there is no overlap.)

2)    a) The probability of drawing the red marble is:
15/(15+10+7+12)=15/44.The probability of         drawing the
blue marble is: 10 / (15+10+7+12) =10/44. P(red or blue)
=15/44+10/44=25/44. (Note: we can sum the probabilities
because there is no overlap.)

b) Not blue or not white means a marble of any color (since
any color marble is either not blue or not white), the
probability of such an event is one.

3)     a) The probability to draw a heart is 13/52, to draw a
nine is 4/52, but note if we just add the numbers, the nine of
hearts is counted twice.Thus, P(heart or nine)= 13/52 +4/52-
1/52=16/52=4/13. (Note: we must subtract from the sum of
the probabilities because there is an overlap from the nine of
hearts.

b) The probability of the card with the human face is P(J or Q
or K)=3*4/52, and the probability of a spade is P(spade)
=13/52.Then, the probability of the card with the human face
or spade is P=12/52+13/52-3/52=23/52, where 3/52 is the
probability of a card being simultaneously (J or Q or K) AND
a spade.

c) “Not 10” means 12 different types of cards, each with four
different suits. One of these suits (spade) has to be excluded.
Then the probability will be 12*3/52=9/13.