Question

A box contains 15 resistors. Twelve of them are labelled 50Ω and the other three are labeled 100Ω. Express the answers in decimals.

1a. What is the probability that the first resistor is 100Ω?

1b. What is the probability that the second resistor is 100Ω, given that the first resistor is 50Ω?

1c. What is the probability that the second resistor is 100Ω, given that the first resistor is 100Ω?

Answer 1

A box contains 15 resistors. Twelve of them are labelled 50Ω and the other three are labeled 100Ω.

1a)

Out of 15 resistors, three are labeled 100Ω.

The probability that the first resistor is 100Ω is

P(100Ω) = 3/15

P(100Ω) = 1/5

1b)

We are given that first resistor is 50Ω. Total number of resistors, after first selection changes to 15 - 1 = 14. Out of 14 resistors, 3 are labeled 100Ω. The probability that the second resistors is 100Ω given that first resistor is 50Ω is

P(100Ω|50Ω) = 3/14

1c)

We are given that first resistor is 100Ω. After first selection, total number of resistors changes to 15 - 1 = 14 and now 3 - 1 = 2 are labeled 100Ω. The probability that the second resistor is 100Ω given that first resistor is 100Ω is

P(100Ω|100Ω) = 2/14

P(100Ω|100Ω) = 1/7