Independent and Dependent Events Worksheet

10.8 Probability of Independent and Dependent Events Now you will see the word "AND" because you are finding the probability of MORE THAN ONE event. When there is more than one event occurring, you multiply the probabilities together. ALWAYS assume you pick what you want. Probabilities of More than One Event: P(Aan * dB) = P(A) * P(B) Independent Events: Events are not related ➤ With replacement: whatever is picked is put back before second pick Denominator stays the same Dependent Events: Events are related Without replacement: whatever is picked is NOT put back before second pick Denominator decreases by one How many fractions should I multiply? You should multiply the same number of fractions as the number of objects you are choosing Examples: Order is Specified 1) Out of a class of 20 students, your teacher chooses students at random to present their projects. What is the probability that she chooses you first, and then chooses Kim second? w/o replacemant P(ypu) * P(kim) *denominator decreases by 1 1/20 * 1/19 = boxed 1 380 2) You flip a fair coin. What is the probability that it shows heads on the first flip and shows tails on the second flip? #denominator stays the same P(H) * P(7) 1/2 * 1/2 = boxed 1 4 3) Tom has 4 navy socks and 6 black socks in a drawer. One dark morning, he randomly pulls out 2 socks. What is the probability that he will select a pair of navy socks? total: 10 socks P(rayy)* P(ne / y) 4/10 * 3/9 = 12/90 = boxed 2 15 *w/o replacement *denominator decreases by 1 *picking same color-numerator also decreases by 1 4) There are 2 glasses of root beer and 4 glasses of cola on the counter. Dave drinks two of them at random. What is the 2 glasses of cola? total: to glasses P(cola)* P(cola) 4/6 * 3/5 = 12/30 = boxed 2 5 #wlo replacement *denominator decreases by 1 picking same flavor-numerator also decreases by 1. 5) Steve reaches into a bag with 5 red marbles, 3 yellow marbles, and 2 green marbles, and randomly selects one. Then, he puts the marble back, and Sam reaches into the same bag and randomly selects a marble. What is the probability that both guys selected a yellow marble? total: 10 marbles #with replacement denominator stays the same P(yellow 3/10 * 3/10 = boxed 9 100 6) A bowl contains 4 tangerines and 5 clementines. John randomly selects one piece of fruit, and then Pam randomly selects one of the remaining pieces of fruit. What is the probability that John selects a tangerine and Fam selects a clementine? w/o replacement *9 total P(targerine)* P(clementine) 4/9 * 5/8 = 20/72 = boxed 5 18 denominator decreases by 1 7) A green die and red die are tossed. What is the probability that a "4" shows on the green die and a "5" shoes on the red die? P(4) * P(5) 1/6 * 1/6 = boxed 1 36 8) You are playing a game that involves spinning the money wheel shown. During your turn, you get to spin the wheel twice. What is the probability that you get more than $500 on your first spin and then go bankrupt on your second spin? 24 total 5150 A 1359 P(more than $500) P(bankrupt) 8/24 * 2/24 = 16/576 = boxed 1 36 9) A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles: a) with replacement P (red) * P (red) 5/12 * 5/12 = boxed 25 144 b) without replacement 12. total P (red) * P (red) 5/12 * 4/11 = 20/132 = boxed 5 33 10) A bag contains 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles, replacing each one before drawing the next. What is the probability of drawing a red, then a blue, and then a white marble? 15 total with replacement P (red) * P(biue)* P(whife) 3/15 * 5/15 * 7/15 = 105/3375 = boxed 7 225 11) There are 6 pennies, 9 nickels, and 3 dimes in a box. Find the probability of... 18 total a) P(2 nickels)-without replacement: b) P(1) nickel and then a dime)-with replacement: P(N) * P(N) 9/18 * 8/17 = 72/306 = boxed 4 17 P(N) * P(D) 9/18 * 3/18 = 27/324 = boxed 1 12 c) P(1 nickel and then 1 dime)-without replacement: P(N) * P(D) 9/18 * 3/17 = 27/306 = boxed 3 34 d) P(1 penny and then 2 nickels)-without replacement: P(P) * P(N) * P(N) 6/18 * 9/17 * 8/16 = 432/4896 = boxed 3 34 12) From a standard deck of cards, what is the probability of choosing..... a) a red and then a club with replacement? P (red) * P(club) 26/52 * 13/52 = 338/2104 = boxed 1 8 b) a 3, then a 7, then a face card w/o replacement? P(3) P(7).P(face card) 4/52 * 4/51 * 12/50 = 192/132600 = boxed 8 5525 b) a diamond, then a heart, then a black card w/o replacement? d) a number card and then a face card with replacement? P( emptyset)* P(∞) * P(biack) 13/52 * 13/51 * 26/50 = 4394/132600 = boxed 169 5100 P( ne)* P(foce ord ) 36/52 * 12/52 = 432/2704 = boxed 27 169