Christopher mixes the letters S, E, L, E, C, T, E, and D 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. three-eighths, 0.375, 37.5%
B. start fraction 3 over 5 end fraction, 0.6, 60%
C. start fraction 5 over 8 end fraction, 0.625, 62.5%
D. one-half, 0.5, 50%
There are 8 letters in total. To find the probability of not selecting a consonant, we first need to find how many consonants are in the group of 8 letters.
The consonants are S, L, C, T, and D. There are 5 consonants out of 8 total letters. Therefore, there are 8 - 5 = 3 vowels in the group.
The probability of not selecting a consonant is just the probability of selecting a vowel, which is 3/8.
This can be expressed as a decimal: 0.375
And as a percentage: 37.5%
Therefore, the answer is (A) three-eighths, 0.375, 37.5%.
Suppose you have a wallet with $5 bills, $10 bills, and $20 bills. If the probability of picking a $10 bill is start fraction 4 over 15 end fraction, and the probability of picking a $5 bill is one-third, what is the probability of picking a $20 bill?
A. Start Fraction 1 over 15 End Fraction
B. start fraction 1 over 5 end fraction
C. start fraction 4 over 15 end fraction
D. two-fifths
Let's start by using algebra to set up two equations based on the given probabilities. Let x be the probability of picking a $5 bill, y be the probability of picking a $10 bill, and z be the probability of picking a $20 bill.
We know that:
y = start fraction 4 over 15 end fraction
x = one-third
We also know that the sum of these probabilities must be 1:
x + y + z = 1
Substituting the known values, we get:
one-third + start fraction 4 over 15 end fraction + z = 1
Multiplying both sides by 15 to get rid of the fractions, we get:
5 + 4 + 15z = 15
Simplifying, we get:
15z = 6
z = start fraction 2 over 5 end fraction
Therefore, the probability of picking a $20 bill is 2/5, which is answer choice (D).
To find the probability that Allen will not select a consonant, we need to determine the number of non-consonant letters and divide it by the total number of letters.
First, let's identify the consonant letters within the given letters: S, L, C, T, and D.
We can see that out of the 8 letters, there are 5 consonants (S, L, C, T, and D) and 3 non-consonants (E, E, and E).
The probability of not selecting a consonant is equal to the number of non-consonant letters (3) divided by the total number of letters (8).
Expressing this probability as a fraction, we get 3/8. As a decimal, it is 0.375, and as a percentage, it is 37.5%.
So, the answer is A. Three-eighths, 0.375, 37.5%.