A bakery has plain, chocolate, apple and cherry croissants. How many ways are th

Question

A bakery has plain, chocolate, apple and cherry croissants. How many ways are there to select: a) 12 croissants? b) 12 croissants, if there has to be at least one of each type? 14. A student randomly guesses on every question on a quiz. There were 5 multiple choice questions each with four possible answers. a) What is the probably that the student answered all the questions correctly? b) What is the probably that the student answered all the questions incorrectly? c) What is the probability that the student got at least one question correct? 15. A single card is chosen randomly from a standard deck of cards. a) What is the probability that the card drawn is an ace? b) What is the probability that the card drawn is a heart? c) What is the probability that the card drawn is an ace or a heart? 16. Use Bayes' Theorem P(F)E) = P(E/F)P(F)/P(E/F)P(F)+P(E/F)P(F) to solve: A drug test will detect actual drug use 95% of the time. However 15% of nonusers will also test positive. If 10% of these being tested use drugs, find the probability that a person used drugs, given that they tested positive for drug use.

Explanation / Answer

14) TOTAL WE HAVE 5 QUESTION

EACH QUESTION HAS 4 OPTIONS

ONLY ONE OPTION IS CORRECT

SO PROBABILITY OF CORRECT ANSWER = 1/4 = 0.25

PROBABILITY OF WRONG ANSWER = 0.75

A) P(ALL ARE CORRECT) = 5C5*(0.25)^5*(0.75)^0 = 0.00097

B) P( ALL ARE INCORRECT) = 5C5*(0.25)^0*(0.75)^5 = 0.2373

C) P( AT LEAST ONE QUESTION CORRECT) = 1 - P( ALL ARE INCORRECT) = 1 -0.2372 = 0.7627

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