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# Disc9 - Math 17C Kouba Discussion Sheet 9 1 Consider a...

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Unformatted text preview: Math 17C Kouba Discussion Sheet 9 1.) Consider a basket containing 5 yellow and 7 black kittens. Close your eyes, reach in, and pick two kittens without replacement. What is the probability that a.) the 1st kitten is black ? b.) the 2nd kitten is black given that the lst kitten is (yellow ? c.) the 2nd kitten is yellow ? ? d.) the 2nd kitten is yellow given that the 1st kitten is yellow ? e.) the 2nd kitten is black ? ‘ 2.) Consider a standard 52-card deck of playing cards. A face card is any Jack, Queen, or King. Pick three cards without replacement from the deck. What is the probability that a.) the 1st card is a face card 7 ' b.) the 2nd card is a face card given that the ﬁrst card is a face card ? c.) the 2nd card is a not face card ? d.) the 3rd card is not a face card given that the ﬁrst card is a face card ? e.) the 3rd card is a face card ? f.) the 3rd card is not a face card given that the 2nd card is not a face card ? 3.) A bag contains 1 blue, 2 white, and 3 red balls. Select 3 balls without replacement. What is the probability that the a.) the 1st ball is red ? b.) the 2nd ball is red given that the lst ball is White ? c.) the second ball is red ? ,3 d.) the third ball is white given that the second ball is blue ? e.) the 3rd ball is red ? f) the 3rd ball is blue ? 4.) Pick 2 cards from a standard deck of playing cards. Let A be the event that the 1st card is a 3 or 4. Let B be the event that the 2nd card is a Jabk, Queen, or King. Determine if A and B are independent events. 5.) Assume that the probability a newborn is a boy is exactly 1 / 2 and the probability it’s a girl is exactly 1 / 2. If gender outcomes from child to child are independent, what is the probability that a family of 5 children will consist a.) of all girls ? b.) of 4 boys and 1 girls ? c.) of 3 girls and 2 boys ? d.) at least 1 girl ? 6.) LeBron James of the Miami Heat shoots ﬁeld goals at the rate of 0.510. Assuming that his shots are independent events, what is the probability that he will a.) make 5 shots in a row ? b.) miss 4 shots in a row 0.) make exactly 5 out of 6 shots ? d.) make exactly 12 out of 21 shots ? e.) make at least 1 out of 10 shot ? 7.) In an NBA playoff game against the Oklahoma City Thunder power forward Dirk Nowitzki of the Dallas Mavericks made 24 out of 24 free throws ! Dirk shoots free throws at the rate of 0.892. Assuming that his shots are independent events, what is the probability that he will a.) make 24 out of 24 shots ? b.) miss 4 shots in a row ? c.) make exactly 4 out of 6 shots ? d.) make at most 8 out of 10 shots ? 8.) You have 15 decks of standard playing cards. Randomly select 1 card from each deck. What is the probability that there will be at least 1 matching pair (same suit and same face value) ? l 9.) A blood test for the HIV virus shows a positive (+) result in 98% of all cases when the virus is actually present in an individual and in 6% of all cases when the virus is NOT present in an individual (false positive). Assume that 1 out of every 250 people are carriers of the virus. a.) What is the probability that a person tests positive given that the person is a carrier of the HIV virus ? Assuming that these tests are independent events, what is the probability that a carrier tests positive twice ? three times ? What is the probability that a non-carrier tests positive ? twice ? three times ? b.) (Law of Total Probability) If a person is selected at random and this test is administered, What is the probability that the test result is positive (+) ? Assuming that these tests are independent events, what is the probability that the same person tests positive twice ? three times ? What is the probability that the same person tests negative? twice ? three times ? 10.) (Genetics— Mendel’s First Law) Gregor Mendel (Austria 1856) studied pea plants and the color of their ﬂowers determined by two genes in their chromosomes. Assume that the following genotypes are possible : CC, Cc (same as CC), and cc, where types CC and Cc produce red ﬂowers and type cc produces white ﬂowers. Suppose that you have a batch of red— and white-ﬂowering pea plants, where all three genotypes CC, Cc, and cc are represented. Assume that 15% of the plants are type CC, 30% of the plants are type Cc, and 55% of the plants are type cc. You will pick 1 parent plant at random from the batch and cross it with a pea plant of genotype cc. a.) What is the probability that the offspring will have red ﬂowers ? white ﬂowers ? b.) What is the probability that the batch parent plant was of genotype Cc given that offspring had red ﬂowers ? ' +++++++++++++++++++++++++++++++++ ” Gravitation is not responsible for people falling in love.” — Albert Einstein ...
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