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a6 Foreign-language study. Choose a student in a U.S. 12. public high school at random and ask if he or she is studying a language other than English. Here is the distribution of results: Language Spanish French German All others None 12 Probability 0.30 0.08 0.02 0.03 (a) Explain why this is a legitimate probability model. (b) What is the probability that a randomly chosen student is studying a language other than English? (c) What is the probability that a randomly chosen student is studying French, German, or Spanish

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Answer #1

Answer:

a).

The probabilities must satisfy

The probability of each outcome is between 0 and 1 inclusive.

The probabilities of all the outcomes add up to 1.

All given probabilities are between 0 and 1.

\sum p = 0.30+0.08+0.02+0.03+0.57 = 1

Sum of the probabilities =1.

Therefore this is a legitimate probability model.

b).

P(other than English) = 0.30+0.08+0.02+0.03

=0.43

c).

P( French,German,Spanish) = 0.30+0.08+0.02

= 0.40

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