Two baskets contain snacks. The basket contain 12 bags of peanuts, of which 5 are reduced sodium and 8 granola bars, of which 2 are reduced sodium. If you randomly select one snack from each basket, what is the probability that both snacks are reduced sodium and 1 snack is a bag of peanuts and the other is a granola bar?

Question

Tanner Snow

Mathematics

27 December, 22:19

Two baskets contain snacks. The basket contain 12 bags of peanuts, of which 5 are reduced sodium and 8 granola bars, of which 2 are reduced sodium. If you randomly select one snack from each basket, what is the probability that both snacks are reduced sodium and 1 snack is a bag of peanuts and the other is a granola bar?

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Aldo Johnston · Answer 1

There are a total of 20 snacks in each bag. We consider the probability of picking a bag of peanuts with reduced sodium and then a granola bar with reduced sodium, then multiply by 2 (because we could pick them in the other order).

There is a 5/20 chance of picking a sodium-reduced bag of peanuts first, and a 2/20 chance of picking a sodium-reduced granola bar next. Thus, the chance of picking them together in that order is 5/20*2/20=10/400, or 1/40. Because we could pick the snacks in either order, we multiply by two, for a result of a 1/20 probability.