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Probability Question 1 In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black. (a) Determine the probability that the metal ball falls into a green slot Solution: G= The event of a metal ball falling in a green slot Sample space= 0,00,1,2,…,36 Number in sample space=38 P(G)=N(G)/N(S) P(G)=2/38=1/19 Question 1 In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black. (b) Determine the probability that the metal ball falls into a green or red slot Solution: R= The event of a metal ball falling in a green or red slot Sample space= 0,00,1,2,…,36 Number in sample space=38 P(R)=N(R)/N(S) + N(G)/N(S) P(R)=18/38 + 2/38 = 10/19 Question 1 In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black. (c) Determine the probability that the metal ball falls into 00 or a red slot Solution: B= The event of a metal ball falling in a 00 or red slot Sample space= 0,00,1,2,…,36 Number in sample space=38 P(B)=1/38 +18/38 = 19/38 Question 1 In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black. (d) Determine the probability that the metal ball falls into the number 31 and a black slot simultaneously. What term can be used to describe this event? Solution: E= The event of a metal ball falling into the number 31 and a black slot simultaneously. Sample space= 0,00,1,2,…,36 Number in sample space=38 P(E) = 0 The number 31 is odd hence its slot is colored red. There is no way a metal ball can fall into a red slot and a black slot at the same time. This event is described as impossible. Question 2 Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related. (a) What is the probability that a randomly selected traffic fatality that happened between 6:00pm December 30 2005 and 5:59 am January 3,2006 was alcohol related? Solution: A= The event of a traffic fatality being alcohol related P(A)=N(A)/N(S) P(A)=193/454 0.425 Question 2 Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related. (b) What is the probability that a randomly selected traffic fatality that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 was not alcohol related? Solution: A= The event of a traffic fatality being alcohol related N= The event of a traffic fatality not being alcohol related P(A)+P(N)=1 P(N)=1-P(A) P(N)=1-0.425 0.575 Question 2 Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related. (c) What is the probability that two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 were both alcohol related Solution: C= The event of two traffic fatalities being alcohol related P(C)= 193/454 *193/454 0.181 Question 2 Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related. (d) What is the probability that neither of two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 were both alcohol related Solution: N= The event of neither two traffic fatalities being alcohol related P(N)= 261/454 *261/454 0.3306=0.331 Question 2 Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related. (e) What is the probability that of two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006, at least 1 was alcohol related Solution: E= The event of at least 1 of two randomly selected traffic fatality being alcohol related N= The event of neither two randomly selected traffic fatality being alcohol related P(E)+P(N)=1 P(E)=1-P(N) 1-0.3306 0.670 Question 3 The following data represent the birth weights (in grams) of babies born in 2005, along with the period of gestation. Birth Weight (grams) Pre-term Term Post-term Total Less than 1000 29,764 223 15 30,002 1000-1999 84,791 11,010 974 96,775 2000-2999 252,116 661,510 37,657 951,283 3000-3999 145,506 2,375,346 172,957 2,693,809 4000-4999 8,747 292,466 27,620 328,833 Over 5000 192 3,994 483 4,669 Total 521,116 3,344,549 239,706 4,105,371 Question 3 (a) What is the probability that a randomly selected baby born in 2005 was postterm? Question 3 (b) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams? Question 3 (c) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams and was postterm? Question 3 (d) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams or was postterm? Question 3 (e) What is the probability that a randomly selected baby born in 2005 weighed less than 1,000 grams and was postterm? Question 3 (f) What is the probability that a randomly selected baby born in 2005 weighed between 3000 to 3999, given the baby was postterm? Question 4 In a game of Jumble, the letters of the word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the jumble word was LINCEY. How many different arrangements are there of the letters in this word? Solution: There are six possible ways to arrange the word LINCEY. 6! = 720 Question 5 The US Senate Appropriations Committee has 29 members and a subcommittee is to be formed by randomly selecting 5 of its members. How many different committees could be formed? Solution: C 29 5 Qtn: The fixed-price dinner at a restaurant provides the following choices: Appetizer: soup or salad Entrée: baked chicken, broiled beef patty, baby beef liver, roast beef Desert: ice cream or cheese cake CSTEM Web link http://www.cis.famu.edu/~cdellor/math/ Presentation slides Problems Guidelines Learning materials