WPP 10 Problem Solutions
Concept 9: John is at a casino. He sits down at a blackjack table and sees
52 cards set face down before him. If he were to pick one at random,
what is the probability that card will be red?
Solution: In order to solve this problem, you must find the total amount of
cards that he can pick from. In this case, it is 52. Now, we must find out
how many red cards are in a deck of 52 cards. The answer is 26, which is
half of 52. Therefore, if he were to pick up one card, the chances of him
picking up a red card is 50%
Concept 10: John then brings his suitcase upstairs and starts to unpack. His
suitcase contains 6 red shirts and 5 green shirts. If he pulls two out at
random, what is the probability they will both be a green shirt?
Solution: With this problem, you first find the total which is 11 shirts. On his
first attempt, the probability he will pick a green shirt is 5/11. He then
replaces the shirt and then tries another attempt at it. The probability is the
same due to the fact that he replaced the green shirt he took out. So your
final answer would be 20%
Concept 11:John then goes downstairs to the casino lobby after
showering. He now sits down at a poker table and is dealt a 2 card hand
from a deck of 5 hearts and 6 diamonds. What is the probability that his
hand will be 2 hearts?
Solution: First, find the total amount of cards. In this case, 11 cards. The
probability that John will have one heart in his hand is 5/11. However, he is
being dealt a 2 card hand so the first heart would be taken from the pile.
Therefore, his chances of getting a second heart will be decreased to
4/10. We then multiply these two probabilities and get 18%
Concept 12: John decides to then go to his room and order a basket of
fruit that has 6 bananas, 5 apples, and 7 oranges. If a piece of fruit is
chosen at random, what I the probability of getting a banana or an
orange?
Solution: First of all, the total of fruits is 18. His chance of getting a banana
is 6/18. His chance of getting an orange is 7/18. We add the two
probabilities together and get 13/18 chance of getting a banana or an
orange.
Concept 13: John becomes so intrigued by the dealers in the casino, he
decides to buy himself a deck of cards and begins practicing predicting
what card he will draw next. If he chooses a single card, what is the
probability of drawing a queen or a heart?
Solution: To begin with, the total amount of cards is 52 and we are looking
for the probability of John drawing a Queen or a Heart. Therefore, to set up
our equation, we have P(Q or H). The probability of John drawing a queen
is 4/52. His chance of drawing a heart is 13/52. We add these two
probabilities together and get 17/52. However, we must subtract the
probability of him getting a queen that is a heart which is 1/52. Our final
answer should be 16/52
Concept 14: John has finished practicing with his deck of cards and
realizes he wants to play Uno instead. If there are 100 cards in a deck of
Uno with 10 wild cards, 18 red cards, 18 blue cards, 18 green cards, 18
yellow cards, and 18 orange cards, what is the probability of him being
dealt a 12 card hand with a) 2 wild cards; b) 2 wild cards, 5 red cards,
and 5 blue cards?
Solution: This problem requires you to put all the previous concepts
together. We also use nCr. First of all, the deck of Uno has 100 cards and
we are being dealt 12 card hands. Therefore, our divisor should be 100 C
12. Meaning our total cards, C, the amount of cards being in a single
hand. If we are looking for the probability of him being dealt 2 wild cards,
we simply put 10 C 2 because there are 10 total wild cards and we only
want 2. That solves the first part of the problem. The second part will be
multiplied by the first part, 10 C 2. Because we want 5 red cards and 5
blue cards. We have to use nCr as well to determine this. The total amount
of red cards is 18. If we are looking for only 5 of those 18 red cards, we set
up our nCr as 18 C 5. If we are looking for 5 blue cards, we similarly set up
our nCr as 18 C 5. As of right now, our total cards only adds up to 46 and
our total hand adds to 12. Since we are not looking for any of the other
cards, we set up their nCr as 18 C 0 because we need to make the totals
add up to 100 yet we already have the amount of cards for our hand. The
18 cards for green, 18 cards for yellow, and 18 cards for orange are
accounted for but, they are not going to be drawn. In the end, our
equation should look like this: (10 C 2 x 18 C 5 x 18 C 5 x 18 C 0 x 18 C 0 x
18 C 0 )/ 100 C 12. Which in the end, our answer is .03%