Jacob mixes the letters J, K, L, J, K, M, N, and P thoroughly. Without looking, Terry draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that K will not be the letter Terry selects?
A. one-fourth, 0.25, 25%
B. three-fourths, 0.75, 75%
C. Start Fraction 4 over 3 End Fraction, 1.33%, 13.3%
D. start fraction 5 over 8 end fraction, 0.625, 62.5%
There are a total of 8 letters, and Terry has an equal chance of drawing any one of them.
There are 2 K's out of 8 letters, so the probability of Terry drawing a K is 2/8 or 1/4.
Therefore, the probability of Terry not drawing a K is 1 - 1/4 = 3/4.
Expressed as a fraction, decimal, and percentage, this is:
$\frac{3}{4}$, 0.75, 75%
The answer is $\boxed{\textbf{(B)}}$.
Adam mixes the letters R, E, A, D, I, N, G, S, and A thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
A. Start Fraction 9 over 5 End Fraction, 1.8, 18%
B. nine-fourths, 2.25, 22.5%
C. four-ninths, 0.444, 44.4%
D. start fraction 5 over 9 end fraction, 0.556, 55.6%
Out of the 9 letters, there are 5 consonants (R, D, N, G, and S) and 4 vowels (E, A, I, and the second A).
Therefore, the probability of Allen selecting a consonant is 5/9.
The probability of Allen not selecting a consonant is the complement of this probability, which is 1 - 5/9 = 4/9.
Expressed as a fraction, decimal, and percentage, this is:
$\frac{4}{9}$, 0.444, 44.4%
The answer is $\boxed{\textbf{(C)}}$.
Suppose you have a drawer full of white, black, and yellow pairs of socks. If the probability of picking a white pair of socks is four-ninths, and the probability of picking a black pair of socks is
start fraction 7 over 18 end fraction, what is the probability of picking a yellow pair of socks?
A. start fraction 1 over 6 end fraction
B. Start Fraction 5 over 12 End Fraction
C. Start Fraction 7 over 15 End Fraction
D. Start Fraction 16 over 27 End Fraction
We know that the sum of the probabilities of picking a white, black, and yellow pair of socks is 1. Therefore, we can use this fact to find the probability of picking a yellow pair of socks:
P(white) + P(black) + P(yellow) = 1
We are given that:
P(white) = 4/9
P(black) = 7/18
Substituting these values into the equation above, we get:
4/9 + 7/18 + P(yellow) = 1
Multiplying both sides by 18, we get:
8 + 7 + 18P(yellow) = 18
Simplifying and solving for P(yellow), we get:
18P(yellow) = 3
P(yellow) = 1/6
Therefore, the probability of picking a yellow pair of socks is:
$\frac{1}{6}$, which is answer choice $\boxed{\textbf{(A)}}$.
The sample space for a roll of two number cubes is shown in the table.
A 6 by 6 table of ordered pairs is shown.
• A single ordered pair appears in each cell of the table.
In row one, the first element of each ordered pair is 1. This pattern continues through row 6, where the first element in each ordered pair is 6.
• In column one, the second element in each ordered pair is 1. This pattern continues through column 6, where the second element in each ordered pair is 6.
What is the probability that the roll will result in two odd numbers?
A. one-ninth
B. one-fourth
C. one-third
D. start fraction 4 over 9 end fraction
There are a total of 6 x 6 = 36 possible outcomes when rolling two number cubes.
We want to count the number of outcomes where both numbers are odd. There are 3 odd numbers on each cube (1, 3, and 5), so there are 3 x 3 = 9 outcomes where both numbers are odd.
Therefore, the probability of rolling two odd numbers is 9/36 or 1/4.
Expressed as a fraction, decimal, and percentage, this is:
$\frac{1}{4}$, 0.25, 25%
The answer is $\boxed{\textbf{(B)}}$.
The sample space for a roll of two number cubes is shown in the table.
A 6 by 6 table of ordered pairs is shown.
• A single ordered pair appears in each cell of the table.
In row one, the first element of each ordered pair is 1. This pattern continues through row 6, where the first element in each ordered pair is 6.
• In column one, the second element in each ordered pair is 1. This pattern continues through column 6, where the second element in each ordered pair is 6.
The two numbers rolled can be added to get a sum. Find P(sum is greater than 5).
A. Start Fraction 5 over 6 End Fraction
B. thirteen-eighteenths
C. Start Fraction 5 over 18 End Fraction
D. one-third
To find the probability that the sum is greater than 5, we can count the number of outcomes where this is the case.
If we examine the table, we can see that there are 11 possible outcomes where the sum is greater than 5:
(1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3)
There are a total of 6 x 6 = 36 possible outcomes when rolling two number cubes. Therefore, the probability of the sum being greater than 5 is 11/36.
Expressed as a fraction, decimal, and percentage, this is:
$\frac{11}{36}$, 0.306, 30.6%
The answer is $\boxed{\textbf{(B)}}$.
You are packing for a vacation. You pack 3 pairs of shorts, 5 shirts, and 2 pairs of shoes. How many different outfits will you be able to make using one pair of shorts, one shirt, and one pair of shoes?
A. 10
B. 17
C. 30
D. 35