Question

(d) What is the probability that at least two players receive exactly two hearts? 7. A hand of 6 cards is drawn from a standard 52 card deck. (a) What is the probability of getting three different pairs? (ex: aabbcc) (b) What is the probability of getting two pairs? (ex: aabbcd) (c) What is the probability of getting three of a kind? (ex: aaabcd) (d) What is the probability of getting all cards with the same suit? 8. A bag contains 7 red marbles, 8 green marbles and 10 blue marbles. Five marbles are (a) If it's known that the first two of the marbles are bluc, what is the probability that the other three marbles are red? (b) If it's known that the first marble is green, what is the probability that the last marble is also green? (c) If it's known that none of the marbles are red, what is the probability that there are more green marbles than randomly drawn from the bag. blue marbles? (d) If it's known that there are the same numbers of red and green marbles, what is the probability that only one of the marbles is blue? 9. John is currently taking a calculus class, and he will have a test next week. He estimates that if he studies over the weekend, he will have 70 % chance to pass the test, and if he doesn't study chance to pass the test. Assume John's estimation is correct, and John has a 90% chance to study over the weekend (a) What is the probability that John will pass the test? (b) If it's known that John passes the test, what is the probability that he doesn't study (c) If it's known that John fails the test, what is the probability that he studies over the weekend? over the weekend, he only has 20 % over the weckend? 10. Box A has 3 green marbles and I red marble, box B has 4 green marbles and 2 red marbles, and box C has 5 green marbles and 3 red marbles. Peter rolls a die first. If the die comes up I, then he will randomly choose a marble from box A; if the die comes up 2 or 3, he will randomly choose a marble from box B; if the die comes up 4, 5 or 6, he will randomly choose a marble from box C. (a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?

Answer 1

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