Question

A pharmacist has filled a box with six different kinds of antibiotic capsules. There are a total of 300 capsules, which are distributed as follows: tetracycline (15), penicillin (30), minocycline (45), Bactrim (60), streptomycin (70), and Zithromax (80). She asks her assistant to mix the pills thoroughly and to withdraw a single capsule from the box. What is the probability that the capsule selected is:

a. Either penicillin or streptomycin?
b. Neither Zithromax nor tetracycline?
c. Bactrim?
d. Not penicillin?
e. Either minocycline, Bactrim, or tetracycline?

Answer 1

A) 1/3

B) 41/60

C) 1/5

D) 9/10

E) 2/5

Step-by-step explanation:

Tet=15

Pen=30

Min=45

Bac=60

Str=70

Zit=80

Total=300

A) Pen and Str = 30+70 = 100

Total= 300

100/300

Answer: 1/3 probability ratio

B) Not Zit or Tet so: Str, Bac, Min, and Pen

30+45+60+70= 205

Total= 300

205/300

Answer: 41/60 probability ratio

C) Bac so: 60

Total=300

60/300

Answer: 1/5 probability ratio

D) Not Pen so: Tet, Min, Bac, Str, and Zit

15+45+60+70+80=270

Total= 300

270/300

Answer: 9/10 probability ratio

E) Min, Bac, and Tet: 45+60+15=120

Total= 300

120/300

Answer: 2/5 probability ratio

For each answer, I calculated the number of pills it could be, and then divided by the total number. I then simplified the ratio for the final answer.

The most likely to be chosen by far is D; there is a 9/10 probability that the pill chosen will not be penicillin.

Answer 2

To find the probability, divide the number of capsules of interest by the total number of capsules.

Step-by-step explanation:

To find the probability of selecting a capsule, we need to divide the number of capsules of interest by the total number of capsules.

a. The number of penicillin capsules is 30 and the number of streptomycin capsules is 70, so the total is 30 + 70 = 100. The probability of selecting either penicillin or streptomycin is 100/300 = 1/3 or approximately 0.333.

b. The number of Zithromax capsules is 80 and the number of tetracycline capsules is 15, so the total is 80 + 15 = 95. The probability of selecting neither Zithromax nor tetracycline is 205/300 = 41/60 or approximately 0.683.

c. The number of Bactrim capsules is 60. The probability of selecting Bactrim is 60/300 = 1/5 or 0.2.

d. The number of penicillin capsules is 30. The probability of not selecting penicillin is 270/300 = 9/10 or 0.9.

e. The number of minocycline capsules is 45, the number of Bactrim capsules is 60, and the number of tetracycline capsules is 15. The total is 45 + 60 + 15 = 120. The probability of selecting either minocycline, Bactrim, or tetracycline is 120/300 = 2/5 or 0.4.