Probability Study Guide Date Block

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1 Probability Study Guide Name Date Block In a regular deck of 52 cards, face cards are Kings, Queens, and Jacks. Find the following probabilities, if one card is drawn: 1)P(not King) 2) P(black and King) 3) P(black or King) 4)P(black face card) If two cards are drawn without replacement, find the following probabilities: 5)P(both face cards) 6) P(both clubs) 7) P(one is Jack and one is Queen) A jar contains four Red marbles, three Blue marbles, and two White marbles. If two marbles are drawn without replacement, find the following probabilities: 8) P(the first is Red and the second is Blue) 9) P(Red and Blue in any order) 10) P(both are the same color) 11) Donte is playing a card game with a standard 52-card deck. He s hoping for a club or a face card on his first draw. What is the probability that he draws a club or a face card on his first draw? 12) Corrine is playing a board game. To find the number of spaces to move, she rolls a pair of dice. On her next roll she wants doubles or a sum of 10. What is the probability that she rolls doubles or a sum of 10 on her next roll? 13) Students at Rolling Hills High School receive an achievement award for either performing community service or making the honor roll. The school has 500 students and 180 of them received the award. There were 125 students who performed community service and 75 students who made the honor roll. What is the probability that a randomly chosen student at Rolling Hills High School performed community service and made the honor roll?

2 14) A university is offering a two-day conference for high school math teachers. Teachers can register for Monday or Tuesday or both days. The conference coordinator complies the following data: 150 teachers registered for Monday. 95 teachers registered for Tuesday. 210 teachers registered in all. One registered teacher selected at random will win a laptop computer as a door prize. If the selected teacher has registered for both days, he or she will win an additional bonus prize of $500. What is the probability that the university will have to pay the additional bonus prize? Bianca is playing a board game. She spins the spinner and rolls a standard 6-sided die. Let s be the spinner result and let d be the die result. 15) What is the probability that 16) What is the probability that s + d > 3 and s d > 3? s + d > 5 and s d < 10? Ladarius is playing a board game. To find the number of spaces to move, he rolls a pair of dice. 17) What is the probability that Ladarius 18) What is the probability that Ladarius rolls rolls doubles or a sum of 7? a sum that is less than 4 or greater than 5? 19) If the probability that your school s soccer team will win its game tomorrow is 0.5 and the probability that your school s baseball team will win its game tomorrow is 0.6, what is the probability that both your school s soccer and baseball teams will not win their games? A laundry bag contains 5 red, 9 blue, and 6 white socks. Find the probability of picking (without replacement) 20) P(red, red) 21) P (blue, blue) 22) P(red, blue) 23) (not blue, not blue)

3 What s the probability of 24) drawing a black card from a deck of cards, 25) rolling a sum of 6 or 8 when rolling 2 dice? replacing it, and drawing another black card? 26) drawing a king or a red card from a deck of cards? 27) rolling 2 dice whose sum is even, given that the 1 st die was a 3? Out of 250 students, 90 take AP Calculus, 75 take AP Chemistry, and 35 take both. Find the following: 28) P(Calc) 29) P(neither Calc nor Chem) 30) P(Calc Chem) 31) P(not Chem Calc) In a survey of a group of 68 Finite Math students, 50 said they liked Frosted Flakes, 49 said they liked Cheerios and 46 said they liked Lucky Charms. 27 said they liked all three, 39 said they liked Frosted Flakes and Cheerios, 33 said they liked Cheerios and Lucky Charms and 36 said they liked Frosted Flakes and Lucky Charms. Represent this information on a Venn Diagram. 32) What is the probability of selecting someone who 33) What is the probability of selecting someone only liked Frosted Flakes? who didn t like any of the cereals mentioned?

4 You survey a group of juniors and seniors. The tree diagram relates student s class and whether a student is employed after school. Find each probability. Let I, S, E, U represent junior, senior, employed, and unemployed, respectively. 34) P(E) 35) P(I and U) 36) P(S E) 37) P (J U) 38) (S U) 39) P(J E) In a survey of a group of 68 Finite Math students, 62 liked the movie The Fault in our Stars, 42 liked the movie The Spectacular Now and 55 liked the movie The Perks of Being a Wallflower. 32 of them liked all 3 movies, 39 of them liked both The Fault in Our Stars and The Spectacular Now, 35 of them liked both The Spectacular Now and The Perks of Being a Wallflower and 49 of them liked both The Fault in Our Stars and The Perks of Being a Wallflower. Represent this information on a Venn Diagram and find the following probabilities. 40) P(only like The Fault in our Stars) 41) P (like only The Spectacular Now or The Perks of Being a Wallflower) 42) P (Who like Fault in our Stars like The Perks of Being Wallflower)

5 43) Out of 50 students who exercise regularly, 25 jog, 20 play basketball and 15 swim. 10 play basketball and jog, 5 play basketball and swim, 7 jog and swim and 2 people do all three. How many students do not do any of these activities?

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8 Evaluate each expression 58) 59) 60)

9 61) 62) 63) 64) A license plate consists of 3 letters followed by 3 numbers. The first letter must be a vowel. The second and third must be consonants. The first number must be a 4, 5, or 6 and the remaining 2 numbers can range from 0 9. How many different license plates are possible? 65) A class consist of 34 students. In how many ways can the teacher select a president, vice president, and treasurer? 66) You are required to read any 8 books from a list of fifteen. How many different selections are possible? 67) There are 110 people at a meeting. They each shake hands with everyone else. How many handshakes were there?

10 68) A group of 25 people are going to run a race. The top 8 finishers advance to the finals. 69) 5 out of 13 students will ride in a car instead of a van. 70) A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals. 71) The buses at the Zoomy Express Bus Company depart as scheduled 80% of the time. The buses depart and arrive as scheduled 68% of the time. What is the probability that a Zoomy Express bus arrives as scheduled if it departs as scheduled? 72) A total of 20% of fire department s firefighters are in the Special Units Division. A total of 8% of the department s firefighters are in the Special Units Division and have a college degree? What is the probability that a firefighter in the Special Units Division has a college degree? 73) The coach of the Strikers soccer team has determined that 50% of the players on the team were also on the team last year. The coach also knows that 30% of players on the team were on the team last year and attended soccer camp during the summer. What is the probability that a Striker who was on the team last year attended soccer camp during the summer?