Question

The cafeteria creates pre-made boxed lunches with equal numbers of the following items:

a sandwich made with either white or wheat bread and either roast beef or bologna
a snack that is either chips, popcorn, or pretzels
a drink that is either bottled water or juice
If Gretchen randomly chooses one of the boxed lunches, what is the probability that she will get a roast beef sandwich and popcorn in her box?

Answer 1

The probability is 1/6

Explanation:

Let's define the following events:

A: get a roast beef sandwich.

B: get popcorn.

Given there are 2 possible sandwiches (bologna or roast beef), P(A) = 1/2

Given there are 3 possible snacks (chips, popcorn, or pretzels), P(B) = 1/3

These events are independent, then:

P(A ∩ B) = P(A) * P(B) = 1/2 * 1/3 = 1/6

where P(A ∩ B) means Gretchen gets both a roast beef sandwich and popcorn.

Answer 2

The required probability is,
`\frac {1}{6}`

Explanation:

P(A sandwich is made of roast beef) =
`\frac {1}{2}`

P(A snack is made of popcorn) =
`\frac {1}{3}`

Since, the two events, i. e., 'A sandwich is made of roast beef' and 'A snack is made of popcorn' are independent, so,

P(Gretchen will get a roast beef sandwich and popcorn in her box)

=
`\frac {1}{2} * \frac {1}{3}`

=
`\frac {1}{6}`