Probability

Typical Probability Question: Basic Probability Typical Probability Question: The image to the right shows a spinner labeled with numbers 1-5. What is the probability of the spinner landing on an even number? Probability can be defined as P(A) = number of favorable outcomes number of possible outcomes

Answer Since … P(A) = number of favorable outcomes number of possible outcomes Our favorable outcomes are the even numbers. This would be 2,4. This gives us 2 favorable outcomes. The number of possible outcomes. There are 5 numbers so there are 5 possible outcomes. This would give us a probability of 2/5 or 40%.

Compound Probability on a single event A bag has 6 orange, 5 lemon, 7 cherry, and 2 strawberry flavored Starbursts. If one candy is pulled out at random, what is the probability that it is cherry OR lemon? Find the number of possible outcomes Find the number of favorable outcomes Our probability of pulling either a cherry or a lemon would be 12/20 or 60% P(A) = number of favorable outcomes number of possible outcomes 6+5+7+2=20 7 cherry + 5 lemon = 12 cherry or lemon

MULTIPLE CHOICE: An ordinary deck of cards has 4 suits: hearts, diamonds, clubs and spades. Each suit has 13 different cards, so there are 52 cards in all. One card is picked at random from the deck. What is the probability that the card’s suit is hearts or clubs? A. 1/16 B. 2/13 C. 1/4 D. 1/2 P(A) = number of favorable outcomes number of possible outcomes Find the number of possible outcomes : 52 Find the number of favorable outcomes : 26 P(A) = 26 52

Make sure you don’t count an item twice!: An ordinary deck of cards has 4 suits: hearts, diamonds, clubs and spades. Each suit has 13 different cards numbered 1 – 10 and J, Q, K A, so there are 52 cards in all. One card is picked at random from the deck. What is the probability that the card is a heart or a 2? P(A) = number of favorable outcomes number of possible outcomes Find the number of possible outcomes : 52 Find the number of favorable outcomes : 13 hearts and 4 2’s BUT one of the 2’s is a heart! So don’t count it twice! 13 hearts + 3 2’s of other suits = 16 favorable outcomes P(A) = 16 52

INDEPENDENT AND DEPENDENT EVENTS when you have more than one event or trial

INDEPENDENT EVENTS 2 TRIALS WHERE ONE OUTCOME DOES NOT EFFECT THE OTHER EXAMPLE: TOSSING A PAIR OF DICE: Find the probability of tossing a 3 on the first die and a 4 on the second die. Calculate each probability INDEPENDENTLY! P(3) = 1 6 P(4) = 1 6 MULTIPLY YOUR TWO PROBABILITIES TOGETHER FOR ONE FINAL ANSWER 1 6 X 1 6 = 1 36

Compound Probability with independent events Carlo brought 8 DVDs with him on vacation. He has 3 comedies, 2 dramas, 2 concerts, and 1 horror movie. Each day he will choose one DVD at random, play it, and return it to the pile. What is the probability that he will watch a comedy on the first day AND a drama on the second day? 1. Find the probability of each event P(comedy) = 3/8 P (drama) = 2/8 or 1/4 This phrase means they are independent events 2. Multiply the probabilities 3/8 * 1/4 = 3/32 The probability of watching a comedy on the first day and a drama on the second day is P(comedy AND drama) = 3/32

Multiple choice Practice Gina has a bag containing 5 red, 4 yellow, and 6 blue tiles that are all the same size and shape. What is the probability of picking a red tile on the first pick, replacing it, and then randomly choosing a yellow tile on the second pick? A. 1/9 B. 3/5 C. 2/21 D. 4/45 P(red) = 5/15 P(yellow) = 4/15 This phrase means they are independent events 5/15 * 4/15 = 20/225

Dependent Probability – 2 trials where one outcome does effect the other Andrew has a box filled with baseball caps. He has 3 blue, 1 green, and 2 black caps. He randomly chooses one cap from the box for himself. Then he picks a second cap out of the box, also randomly, for his little brother to wear. What is the probability that Andrew picked a black cap followed by a green cap? Find the number of possible outcomes for picking a black cap Since Andrew picked his cap out and then didn’t replace it, there are only 5 possible outcomes for picking a green cap P(black)=2/6 or 1/3 P(green)=1/5 P(both)=1/3 * 1/5 = 1/15 3 blue + 1 green + 2 black = 6 total caps 3 blue + 1 green + 1 black = 5 total caps Since he will be wearing the first cap, it is assumed he will NOT be replacing it as he chooses a 2nd cap. This implies the 2nd choice of cap DEPENDS upon what he picks the 1st time.

Independent or dependent? A nickel is tossed, a number cube with faces labeled 1-6 is rolled, and a quarter is tossed. What is the probability that the nickel lands on heads, the number cube shows an odd number, and the quarter lands on tails? A. 1/2 B. 3/10 C. 1/6 D. 1/8 These are independent because a rolling a die has nothing to do with tossing a coin 1/2 * 3/6 *1/2 = 3/24

Mixed probability Favorable = 3 candies total = 13 A box contains 6 chocolate covered cherries, 3 peppermint creams, 2 caramels, and 2 strawberry creams. Find the following: If a single candy is selected, find the probability that it is a peppermint cream. If a single candy is selected, find the probability that it is a peppermint cream or a strawberry cream. If two pieces of candy are selected without replacement, find the probability of getting two caramels Jane is very picky and doesn’t like caramel or strawberry cream. What is the probability that she will pick a caramel, put it back, and then pick a strawberry cream? Favorable = 3 candies total = 13 P(peppermint cream)=3/13 Favorable outcomes = 5 candies total = 13 P(peppermint or strawberry)=5/13 Dependent – not replacing ---- 2/13 * 1/12 = 2/156 or 1/78 Independent – replacing ---- 2/13 * 2/13 = 4/169