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Name: ________________________ Class: ___________________ Date: __________ ID: A Binomial Probability - At Least or At Most - Problem Set Short Answer 2 1. On any given day, the probability that the entire Watson family eats dinner together is . Find the probability 5 that, during any 7-day period, the Watsons eat dinner together at least six times. 3 2. The probability that a planted watermelon seed will sprout is . If Peyton plants seven seeds from a slice of 4 watermelon, find, to the nearest ten thousandth, the probability that at least five will sprout. 3. A mathematics quiz has five multiple-choice questions. There are four possible responses for each question. Jennifer selects her responses at random on every question. What is the probability she will select the correct response for at most one question? What is the probability she will select the correct response to at least three questions? 4. A spinner is divided into two regions, green and red. The probability of the pointer landing on the green region is 2 . The pointer is spun 5 times. What is the probability of the pointer landing on the green region exactly 2 times? 3 What is the probability of the pointer landing on the red region at least 4 times? 1 Name: ________________________ ID: A 5. In each basketball game played, the Raiders have a probability of winning of 2 1 and a probability of losing of . 3 3 Find the probability of the Raiders winning: (1) exactly 4 out of five games (2) at most 4 out of five games (3) exactly 4 out of five games if they have already won the first two games 2 6. The probability of rain on any given day is . What is the probability of at most one day of rain during the next 3 three days? 7. In the accompanying diagram, the circle is divided into five equal sections. Assume an unbiased experiment when a spinner is spun. a b If the spinner is spun once, find: P(B); P(number) If the spinner is spun three times, determine the probability it will land on (1) no B’s (2) at least two numbers (3) no more than one number 2 ID: A Binomial Probability - At Least or At Most - Problem Set Answer Section SHORT ANSWER 1. ANS: 1472 . P(6 dinners) = 78125 PTS: 4 REF: 060331b KEY: at least or at most 2. ANS: 0.7564. P(5 sprouts) = + P(7 dinners) = STA: A2.S.15 + P(6 sprouts) = TOP: Binomial Probability + P(7 sprouts) = PTS: 4 REF: 060529b KEY: at least or at most 3. ANS: 648 106 , 1024 1024 STA: A2.S.15 TOP: Binomial Probability PTS: 7 REF: 019941siii KEY: at least or at most 4. ANS: 40 11 , 243 243 STA: A2.S.15 TOP: Binomial Probability PTS: 10 KEY: spinner 5. ANS: 80 211 4 , , 243 243 9 REF: 088942siii STA: A2.S.15 TOP: Binomial Probability PTS: 10 KEY: mixed 6. ANS: 7 27 REF: 088739siii STA: A2.S.15 TOP: Binomial Probability PTS: 2 REF: 068819siii KEY: at least or at most STA: A2.S.15 TOP: Binomial Probability 1 ID: A 7. ANS: 1 3 64 81 44 , , , , 5 5 125 125 125 PTS: 10 KEY: spinner REF: 088942siii STA: A2.S.15 2 TOP: Binomial Probability