Question

Direction: Read and understand each problem and solve. Show your solution if necessary.

1. There are 3 gold medalist, 5 silver medalist and twelve bronze medalists. One student is randomly chosen for an interview. Find the probability that the student is a silver medalist.

2. A letter is chosen from the word MATHEMATICS. What is the probability that the letter is?
a. consonant?
b. vowel?
c. not a letter A?

3. Suppose the probability that a television is defective is 0.123. What is the probability that a television is not defective? ​

Answer 1

[1] 0.25, 0.25%, or
`(1)/(4)`

We will divide the number of wanted outcomes by possible outcomes.

`\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =(5)/(3+5+12) =(5)/(20) =(1)/(4)`

[2]

We will follow the same steps as problem 1.

MTHMTCS = 7 consonants

AEAI = 4 vowels

MTHEMTICS = 9 letters that are not A's

MATHEMATICS = total of 11 letters

(a)

`\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =(7)/(11)`

(b)

`\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =(4)/(11)`

(c)

`\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =(9)/(11)`

[3] 0.877

If the probability that a television is defective is 0.123, then the probability that a television is not defective is:

1 - 0.123 = 0.877