Green Probability Handout 1 - WordPress.com
Green Probability Handout 1 - WordPress.com
Green Probability Handout 1 - WordPress.com
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<strong>Probability</strong> (Day 1) – <strong>Green</strong> Problems<br />
Suppose you select a letter at random from the words MIDDLE SCHOOL.<br />
Find P(L) and P(not L). First determine the number of possible out<strong>com</strong>es. There are<br />
12 letters in the two words, so there are 12 possible out<strong>com</strong>es when you select a<br />
letter at random. Next determine of favorable out<strong>com</strong>es for P(L). There are two<br />
L’s.<br />
number of favorable out<strong>com</strong>es 2 1<br />
Thus, P(L) = number of possible out<strong>com</strong>es<br />
= 12<br />
= 6<br />
You can find P(not L) several ways. Since there are 12 possible out<strong>com</strong>es and 2 are<br />
L, 12 – 2 = 10 are not L.<br />
number of favorable out<strong>com</strong>es 10 5<br />
Thus, P(not L) = number of possible out<strong>com</strong>es<br />
= 12<br />
= 6<br />
Also P(not L) = 1 - P(L)<br />
1<br />
= 1- 6<br />
= 5 6<br />
A drawer contains 6 red socks, 4 blue socks, and 14 white socks. A sock is pulled<br />
from the drawer at random. Find the probability for each case.<br />
1. Red 2. Blue<br />
3. Red or white 4. Red, white or blue<br />
5. Not red 6. <strong>Green</strong><br />
A spinner numbered from 1 to 20 is spun randomly. Find the probability of where<br />
the spinner lands for each case.<br />
7. 17 8. An odd number<br />
9. A number divisible by 5 10. 26<br />
11. A number with a 1 in it 12. A prime number<br />
13. A number less than 6 14. A number<br />
15. A number that is not less than 17 16. A number divisible by 3 or 4
Find each probability for choosing a letter at random from the word PROBABILITY.<br />
17. P(B) 18. P(P)<br />
19. P(A or I) 20. P(not P)<br />
A box contains 7 red, 14 yellow, 21 green, and 84 purple marbles. A marble is<br />
drawn at random from the box. Find each probability.<br />
21. P(red) 22. P(yellow)<br />
23. P(green or red) 24. P(purple, yellow or red)<br />
25. P(not green) 26. P(not purple, yellow or red)<br />
27. The numerical values around the spinner indicate the<br />
measure of the central angle for each sector of the<br />
circle. Using the fair spinner, what is the probability of<br />
getting “Ahead 3 spaces?” Express your answer as a<br />
<strong>com</strong>mon fraction.<br />
28. What is the probability that a point chosen<br />
inside the largest rectangle is not within a<br />
shaded region? Express your answer as a<br />
<strong>com</strong>mon fraction.<br />
3<br />
1<br />
2 2 2 2 2<br />
2<br />
29. What is the probability of Jonah picking a vowel if he randomly chooses a letter<br />
from the word “CAT?” Express your answer as a <strong>com</strong>mon fraction.<br />
30. There are six bottles of soda, three bottles of juice and one bottle of water in a<br />
cooler. If a bottle is randomly selected from the cooler, what is the probability<br />
that it is the bottle of water? Express your answer as a <strong>com</strong>mon fraction.<br />
31. Top Notch Nose Contest<br />
Schnoz Elementary School decided to hold a Top Notch Nose Contest as a
fundraising activity. Each contestant submitted a photograph of his or her pet<br />
featuring the pet’s nose, along with an entrance fee of $1.00.<br />
Half of the photographs submitted were pictures of cats. A quarter of the<br />
photographs received were pictures of dogs, 1/8 were pictures of horses, 1/16 were<br />
pictures of rabbits, and 13 were gerbils. Only 1/32 of the photos were picture of<br />
birds.<br />
How many photos of pets were entered in the contest?<br />
Extra: If each pet had an equal chance of winning, what’s the probability that a<br />
rabbit’s photograph was the winner?<br />
<strong>Probability</strong> (Day 1) – <strong>Green</strong> Solutions<br />
1. 1<br />
4<br />
3. 5<br />
6<br />
5. 3<br />
4<br />
7. 1<br />
20<br />
9. 1<br />
5<br />
11. 11<br />
20<br />
13. 1<br />
4<br />
15. 1<br />
5<br />
17. 2<br />
11<br />
19. 3<br />
11<br />
21. 1<br />
18<br />
23. 2<br />
9<br />
2. 1<br />
6<br />
4. 1<br />
6. 0<br />
8. 1<br />
2<br />
10. 0<br />
12. 2<br />
5<br />
14. 1<br />
16. 1<br />
2<br />
18. 1<br />
11<br />
20. 10<br />
11<br />
22. 1<br />
9<br />
24. 5<br />
6
25. 5<br />
6<br />
26. 1<br />
6<br />
27. Since “Ahead 3 spaces” occupies 100 degrees out of the 360 degrees in the circle,<br />
the probability that the spinner will land there is 100 = 10 =<br />
5 .<br />
360 36 18<br />
28. There are three different-sized regions within the rectangle. Notice that there<br />
are five of each size, and one of each size is shaded. Since 1 5<br />
of each set is shaded,<br />
then 1 5<br />
of the entire rectangle is shaded, and the probability of choosing a point<br />
within a shaded region is also 1 . The probability of choosing a point not within a<br />
5<br />
shaded region, then, is<br />
1 4<br />
1 − = .<br />
5 5<br />
29. There are three letters in the word ‘CAT’, only one of which is a vowel. Thus, the<br />
probability of Jonah picking a vowel at random is one out of three or 1/3.<br />
30. The bottle of water is one of the 10 bottles, so the probability that a randomly<br />
selected bottle is the water bottle is 1/10.<br />
31. There were 416 photographs of pets entered in the contest.<br />
*EXTRA* - The probability that a rabbit’s photograph was the winner is 26/416 =<br />
1/16.<br />
What I did was do the problem in language first. X = Total number of pets. So, X =<br />
Cats (x) + Dogs (x) + Horses (x) + Rabbits (x) + Birds (x) + Gerbils. Then, I<br />
substituted them for numbers. Then I added 1/2x + 1/4x + 1/8x + 1/16x + 1/32x +<br />
13. When I added all of the fractions, the sum was 31/32. The equation was now X =<br />
31/32x from 31/32x and from X. Now, the equation was 1/32x = 13. To get X alone,<br />
I divided 1/32 from both X and 13. For X, the quotient I got was 416. That was how<br />
many animals were entered in the contest.<br />
*EXTRA* - There are 26 rabbits. I got 1/16 as the probability that a rabbit’s photo<br />
was the winner by doing 26/416 and I simplified the fraction.
Bibliography Information<br />
Teachers attempted to cite the sources for the problems included in this problem set. In some<br />
cases, sources were not known.<br />
Problems<br />
Bibliography Information<br />
31<br />
The Math Forum @ Drexel<br />
(http://mathforum.org/)<br />
27 - 30 Math Counts (http://mathcounts.org)<br />
1 - 26<br />
Davison, David M. Prentice Hall Pre-<br />
Algebra Tools for a Changing World.<br />
Needham, Mass: Prentice Hall, 2001.<br />
Print.