Question

A small monster collector has captured ten Bagel-type small monsters. Each Bagel-type small monster has a 35% chance of being a Sesame Seed-subtype and a 20% chance of being a Whole Wheat-subtype.What is the probability of exactly eight of the captured small monsters being Whole Wheat-subtypes?What is the probability of at least one of the captured small monsters being a Sesame Seed-subtype?What is the probability that there are no Sesame Seed- or Whole Wheat-subtype small monsters captured?What is the probability that are at least two Whole Wheat/Sesame Seed dual-subtype small monsters captured?

Answer 1

Answer:

Check the explanation

Explanation:

Each Bagel-type small monster has 0.35 probability of being a Sesame Seed-subtype and 0.2 probability of being a Whole Wheat-subtype.

The probability that exactly 8 of them are Whole Wheat-subtype is $\binom{10}{8}(0.2)^8(0.8)^2$ using multiplication principle, because first need to choose which 8 are Whole Wheat-subtype, and if exactly 8 of them are Whole Wheat-subtype, then other two are not Whole Wheat-subtype. The former has probability 0.2, while the latter has probability 1-0.2 = 0.8 .

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