Question

Due to a packaging error, 4 cans labeled diet soda were accidentally filled with regular soda and placed in a 12 pack carton of diet soda. Two cans were randomly selected from this 12 pack. What is the probability that both cans were regular soda?

Answer 1

1/11

Explanation:

We know that 4 cans filled with regular soda were labelled diet soda and placed in a 12 pack carton.

Two cans were picked randomly and we are to find the probability that both cans were of regular soda.

No. of cans with regular soda = 4

No. of cans with diet soda = 8

P (both cans regular soda) = 4/12 * 3/11 = 1/11

Answer 2

Probability that both cans were regular soda =
`(1)/(11)`

Explanation:

Probability =
`(Desired outcome)/(Total possible outcomes)`

We are given 12 total number of cans; 4 cans have been accidentally filled with diet soda.

Probability that first can is a regular soda:

Outcome that first can is a regular soda will give us the number of regular soda available which are 4

Using formula of probability

Total possible outcomes are, n(total) = 12

Desired outcome: 4 (cans of regular soda)

P(1st can) =
`(4)/(12)` =
`(1)/(3)`

Probability that 2nd can is a regular soda:

As we have already taken a can of regular soda from the pack, the total soda in the pack now 11 and the regular soda left are 3.

Total possible outcomes are, n(total) = 11

Desired outcome: 3 (cans of regular soda as one has already been taken)

P(2nd can) =
`(3)/(11)`

Probability that both cans are regular soda:

P(both) = P(1st can) × P(2nd can)

=
`(1)/(3) * (3)/(11)`

=
`(1)/(11)`