Here is a table showing all 52 cards in a standard deck. Face cards Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Red Hearts AV 2? 3V 4' 5? 6? 7v 8? 9V 10v J? QV K? Red Diamonds AG 20 30 4O 50 60 70 80 99 109 JO Q6 KO Black Spades Ae 29 39 4e 59 69 Te 89 9a 109 J9 Qe K9 Black Clubs A-& 2-!- 3'! 4% 5-!- 61- Tau SI!- 9'! 10'!- J-Ev Q KI!- Suppose a card is drawn at random from a standard deck. The card is then shuffled back into the deck. Then for a second time a card is drawn at random from the deck. The card is then shuffled back into the deck. Finally, for a third time a card is drawn at random from the deck. What is the probability of first drawing a five, then a face card, and then a diamond? Do not round your intermediate computations. Round your final answer to four decimal places. Here is a table showing all 52 cards in a standard deck. is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the Facecards Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Red Hearts AV 2? 3V 4' 5V 6? 7v 8? 9' 10' J? QV K? Red Diamonds Ao 20 39 4o 50 do To 80 99 109 Jo Q9 KO Black Spades Ag 29 39 4e 59 69 79 89 99 109 J9 Q9 K9 Black Clubs A-Ev 2-!- 3-9 4-9 5-!- 6-5- M. 8-!- 9-9 104- J; Q- Ka- Acarc deck. What is the probability that both of the cards are hearts? Do no: round your intermediate computations. Round your final answer to four decimal places. An urn contains 9 green and 8 white balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are green? Round your answer to three decimal places. XA local high school has both male and female students. Each student either plays a sport or doesn't. The twoway table summarizes a random samp e of 80 students. Female Male No sport 12 15. Sport 36 l? Let sport be the event that a randomly chosen student (from the table} plays a sport. Let female be the event that a randomly chosen student [from the table) is female. Find the following probabilities. Write your answers as decimals. {5.) P(female) = :l {b} P{sport and female) = (c) P{sport | female) = X 53 Suppose that 3% of all adults suffer from diabetes and that 28% of all adults are obese. Suppose also that 1% of all adults both are obese and suffer from diabetes. (a) Find the probability that a randomly chosen adult is obese, given that he or she suffers from diabetes. Round your answer to the nearest hundredth. Calculator (b) Find the probability that a randomly chosen adult who is obese also suffers from diabetes. Round your answer to the nearest hundredth. X 5