Question

common core math 2
probability test review worksheet 2
single event probability
one of these names is to be drawn from a hat. determine each probability below:
mary jenny bob marilyn bill jack jerry tina connie joe

1. p(4 - letter name) = __________ 2) p(name starting with b) = __________
2. p(name starting with t) = __________ 4) p(7 - letter name) = __________
3. p(name starting with s) = __________ 6) p(name ending with y) = __________

one of these cards will be drawn without looking.
10 4 7 j s 9 10 2 m 5 4 j

1. p(5) = ______ 8) p(j) = ____ 9) p(a number) = ______
2. p(4) = ______ 11) p(t) = ____ 12) p(a letter) = ______

one card is drawn from a well - shuffled deck of 52 cards. what is the probability of drawing...

1. p(ace) = ______ 14) p(face card - k, j, q) = ______
2. p(a red 10) = ______ 16) p(not a diamond) = ______

a spinner, numbered 1 - 8, is spun once. what is the probability of spinning...

1. an even number? ______ 18) a multiple of 3? ______
2. a prime number? ______ 20) a 9? ______

Explanation:

Step1: Recall probability formula

The probability formula is $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Names from hat:

Total number of names = 10.

1. P(4 - letter name):

Names with 4 - letters are Mary, Bob, Jack, Joe. So number of favorable outcomes = 4.
$P(4 - letter\ name)=\frac{4}{10}=\frac{2}{5}$

1. P(name starting with B):

Names starting with B are Bob, Bill. So number of favorable outcomes = 2.
$P(name\ starting\ with\ B)=\frac{2}{10}=\frac{1}{5}$

1. P(name starting with T):

Name starting with T is Tina. So number of favorable outcomes = 1.
$P(name\ starting\ with\ T)=\frac{1}{10}$

1. P(7 - letter name):

Names with 7 - letters are Marilyn, Connie. So number of favorable outcomes = 2.
$P(7 - letter\ name)=\frac{2}{10}=\frac{1}{5}$

1. P(name starting with S):

There are 0 names starting with S. So number of favorable outcomes = 0.
$P(name\ starting\ with\ S)=\frac{0}{10}=0$

1. P(name ending with Y):

Names ending with Y are Jenny, Jerry. So number of favorable outcomes = 2.
$P(name\ ending\ with\ Y)=\frac{2}{10}=\frac{1}{5}$

Cards:

Total number of cards = 12.

1. P(5):

There is 1 card with 5. So number of favorable outcomes = 1.
$P(5)=\frac{1}{12}$

1. P(J):

There are 2 cards with J. So number of favorable outcomes = 2.
$P(J)=\frac{2}{12}=\frac{1}{6}$

1. P(a number):

Numbers are 10, 4, 7, 9, 10, 2, 5, 4. So number of favorable outcomes = 8.
$P(a\ number)=\frac{8}{12}=\frac{2}{3}$

1. P(4):

There are 2 cards with 4. So number of favorable outcomes = 2.
$P(4)=\frac{2}{12}=\frac{1}{6}$

1. P(T):

There are 0 cards with T. So number of favorable outcomes = 0.
$P(T)=\frac{0}{12}=0$

1. P(a letter):

Letters are J, S, M, J. So number of favorable outcomes = 4.
$P(a\ letter)=\frac{4}{12}=\frac{1}{3}$

Deck of 52 cards:

1. P(ace):

There are 4 aces in a deck. So number of favorable outcomes = 4.
$P(ace)=\frac{4}{52}=\frac{1}{13}$

1. P(face card - K, J, Q):

There are 12 face - cards (4 Kings, 4 Jacks, 4 Queens) in a deck. So number of favorable outcomes = 12.
$P(face\ card)=\frac{12}{52}=\frac{3}{13}$

1. P(a red 10):

There are 2 red 10s (10 of hearts and 10 of diamonds). So number of favorable outcomes = 2.
$P(a\ red\ 10)=\frac{2}{52}=\frac{1}{26}$

1. P(NOT a diamond):

There are 39 non - diamond cards (13 spades, 13 clubs, 13 hearts). So number of favorable outcomes = 39.
$P(NOT\ a\ diamond)=\frac{39}{52}=\frac{3}{4}$

Spinner numbered 1 - 8:

Total number of outcomes = 8.

1. P(an EVEN number):

Even numbers are 2, 4, 6, 8. So number of favorable outcomes = 4.
$P(an\ EVEN\ number)=\frac{4}{8}=\frac{1}{2}$

1. P(a multiple of 3):

Multiples of 3 are 3, 6. So number of favorable outcomes = 2.
$P(a\ multiple\ of\ 3)=\frac{2}{8}=\frac{1}{4}$

1. P(a PRIME number):

Prime numbers are 2, 3, 5, 7. So number of favorable outcomes = 4.
$P(a\ PRIME\ number)=\frac{4}{8}=\frac{1}{2}$

1. P(a 9):

There are 0 outcomes of 9. So number of favorable outcomes = 0.
$P(a\ 9)=\frac{0}{8}=0$

Answer:

1. $\frac{2}{5}$
2. $\frac{1}{5}$
3. $\frac{1}{10}$
4. $\frac{1}{5}$
5. $0$
6. $\frac{1}{5}$
7. $\frac{1}{12}$
8. $\frac{1}{6}$
9. $\frac{2}{3}$
10. $\frac{1}{6}$
11. $0$
12. $\frac{1}{3}$
13. $\frac{1}{13}$
14. $\frac{3}{13}$
15. $\frac{1}{26}$
16. $\frac{3}{4}$
17. $\frac{1}{2}$
18. $\frac{1}{4}$
19. $\frac{1}{2}$
20. $0$