Liam packs his lunchbox with a sandwich (either peanut butter and jelly (PB&J) or ham and cheese) and a fruit (apple, orange, or banana). He picks one of each at random, without looking. If there's an equal chance of getting any sandwich or fruit, what is the probability he picks a PB&J sandwich and an apple?

Question

Liam packs his lunchbox with a sandwich (either peanut butter and jelly (PB&J) or ham and cheese) and a fruit (apple, orange, or banana). He picks one of each at random, without looking. If there's an equal chance of getting any sandwich or fruit, what is the probability he picks a PB&J sandwich and an apple?
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1/4
1/6
1/5
1/3

GPT 3.5 · Answer

1/6

There are 2 options for the sandwich (PB&J or ham and cheese) and 3 options for the fruit (apple, orange, or banana). This means there are a total of 2 x 3 = 6 possible combinations. Since Liam is picking at random, each combination has an equal probability of 1/6 of being chosen.

The combination of PB&J sandwich and an apple is only one of those 6 combinations, so the probability is 1/6.