Review on Probability
Experimental Probability
# of times event occurs/# of times experiment is done
Theoretical Probability
#of outcomes/total # of possible outcomes
A storeowner made a list of the number of greeting cards sold last month. The store sold 167 thank-you cards, 285 birthday cards, and 56 blank cards. Based on this data, what is the probability that the next customer will by a blank card? (write in decimal)
0.11
If a coin is tossed and a die is rolled at the same time, how many outcomes are possible?
12 outcomes
Draw a tree diagram: You have a choice of three hamburgers, 4 drinks, 2 sides, and 3 desserts. How many outcomes are there?
24 outcomes
What probability was being used in the last question? What kind of event?
Compound probability and an independent event
Compound Probability - what are the two events?
Independent and Dependent
Compound Probability
Made up of more than one event
What is the Theoretical Probability of rolling a six on a die?
P( 6 on die) = 1/6
a card is drawn from a deck of 52 cards, and replaced in a deck. The deck is shuffled and a second card is drawn. What is the probability that both cards are diamonds?
P( D, D) = 13/52 * 13/52 = 1/16
What is the Theoretical Probability of rolling a 6 on a die?
P(6) = 1/6
A die is rolled twenty times and landed on 6 four times. Find the probability of a die rolling on a six.
P(6) = 4/20 = 1/5
You accidentally dropped a coin from the top of the seven stairs. What is the probability that it will land on the sixth step, tails up?
P(6, T) = 1/7 * 1/2 = 1/14
I am picking from a raffle, there are two prizes for two winners. There are 6 names: Bill, Sue, Pam, Bob, Tom, and Lisa. What is the probability of Bill and Sue being picked? What about Tom and Bob?
P(B, G) = 3/6 * 3/5 = 9/30 = 3/10 P(B, B) = 3/6 * 2/5 = 2/10 = 1/5
Each letter of the word ALGEBRA is placed on a slip of paper. You randomly select two slips of paper without replacement. What is the probability you will choose a G followed by a vowel?
P(G,Vowel) = 1/7 * 3/6 = 1/14
What is the theoretical probability of flipping heads? Tails?
P(H) = 1/2 P(T) = 1/2
A box contains two nickels, 3 pennies, 1 dime, and two quarters. Find the probability of choosing first a dime and then, without replacing the dime, choosing a penny.
P(dime, penny) - 1/8*3/7=3/56
A bag has 5 mangoes, 9 oranges, and 4 apples. For your lunch, you choose 2 fruits, one at a time without replacement. What is the probability of getting a mango and an orange?
P(m, o) = 5/18 * 9/17 = 5/34
A toy manufactured by a company consists of two parts. A and B. In the process of the manufacturing of part A, 92 out of 100 are likely to be non-defective. Similarly 89 out of 100 of part B are likely to be non-defective. What is the probability that the toy selected at random is non-defective?
P(nd(A) , nd(B)) = 23/25 * 89/100 = 2047/2500
You are picking a card fro a bag with 1 card for each letter of the alphabet. What is the probability of picking a letter in the word "recede."
P(recede) = 4/26 = 2/13
A leftover Hershey Kiss bag contains 8 gold kisses, 6 silver kisses and 4 red kisses. Find the probability of a student picking a silver kiss, replacing it and then picking a gold kiss?
P(silver, gold) = 6/18 * 8/18 = 4/27
You are making a cake for your friend's birthday. You choose the cake mix and frosting randomly from your pantry. There is chocolate, vanilla, and strawberry cake mix, and vanilla and chocolate frosting. What is the probability you will make a strawberry with vanilla frosting?
P(strawberry, vanilla) = 1/3 * 1/2 = 1/6
There are 12 starbursts: 7 red and 5 yellow. Jesse randomly picks a yellow starburst and replaces it. He then picks a red starburst. Find the probability of this happening
P(y, r) = 5/12 * 7/12 = 35/144
Independent event
Probabilities DO NOT affect each other P(A,B) = P(A) * P(B) "Replace"
Define probability
a number from 0 to 1 that tells how likely something is to happen
A M&M bag contains 6 yellow, 5 brown, 4 green and 5 blue M&M's. Students are allowed to take two M&M's. A.) Find the probability of a student picking a yellow M&M and then a green M&M. B.) Find the probability of a student picking a blue M&M and then another blue M&M. C.) What kind of probability is taking place in "b"?
a.) P(yellow, green) = 6/10 * 4/19 = 6/95 b.) P(blue, blue) = 5/20 * 4/19 = 5/95 = 1/5 c.) Compound probability and a dependent event
Dependent or Independent? a.) Flipping a coin twice b.) choosing a hammer and a paper color in a hardware store c.) selecting a can of corn and a container of juice in a supermarket d.) Picking a board from a pile, nailing it on a fence, then picking another board from a pile
a.) independent b.) independent c.) independent d.) dependent
Dependent Event
probabilities do affect each other