CHAPTER 5 1. Suppose you have a bag of 3 red balls, 1 blue ball, and 2 green bal
ID: 3054042 • Letter: C
Question
CHAPTER 5 1. Suppose you have a bag of 3 red balls, 1 blue ball, and 2 green balls. a. Determine the sample space if you are grabbing two balls out of the bag, one at a time, with replacement. b. Determine the sample space if you are grabbing two balls out of the bag, one at a time, without replacement. What is the probability of grabbing two red balls out of the bag, with replacement? Did you use the classical or empirical approach to calculate this probability? What is the probability of grabbing two red balls out of the bag, without replacement? Did you use the classical or empirical approach to calculate this probability? Suppose you are grabbing two balls out of the bag without replacement. Let the event A be grabbing the first ball and let the B be the event of grabbing the second ball. Are these two events independent or dependent? Disjoint or not disjoint? c. d. e. f. Suppose you are grabbing two balls out of the bag with replacement. Let the event A be grabbing the first ball and let the B be the event of grabbing the second ball. Are these two events independent or dependent? Disjoint or not disjoint?Explanation / Answer
1) Let the balls coded as R1, R2, R3, B, G1, G2
a) Total no of sample space with replacement would be 6^2 = 36. which are: R1R1, R1R2, R1R3, R1B, R1G1, R1G2, R2R1, R2R2, R2R3, R2B, R2G1, R2G2, R3R1, R3R2, R3R3, R3B, R3G1, R3G2, BR1, BR2, BR3, BB, BG1, BG2, G1R1, G1R2, G1R3, G1B, G1G1, G1G2, G2R1, G2R2, G2R3, G2B, G2G1, G2G2.
b) Total no of sample space without replacement would be 6P2 = 30. which are: R1R2, R1R3, R1B, R1G1, R1G2, R2R1, R2R3, R2B, R2G1, R2G2, R3R1, R3R2, R3B, R3G1, R3G2, BR1, BR2, BR3, BG1, BG2, G1R1, G1R2, G1R3, G1B, G1G2, G2R1, G2R2, G2R3, G2B, G2G1.
c) 2 red balls can be chosen from 3 red balls with replacements in 3^2 = 9 ways
Total sample space = 36
Probability of chosing 2 red with replacement = 9/36 = 1/4
d) 2 red balls can be chosen from 3 red balls without replacements in 3P2 = 6 ways
Total sample space = 30
Probability of chosing 2 red without replacement = 6/30 = 1/5
e) As the balls are picked without replacement, in event A, we choose from 6 balls and in event B we choose from 5 balls except the one already picked. So, clearly event A and event B is is not independent.
f) As the balls are picked with replacement, in event A, we choose from 6 balls and in event B also we choose from all the 6 balls. So clearly both the events are independent to each other.
3)
a) Probability that a passenger survived = 711/2224
b) Probability that a passenger was female = 425/2224
c) Probability that a passenger was female or a child = (425+109)/2224= 534/2224
d) Probability that a passenger was female and survived = 316/2224
e) Probability that a passenger was female or survived = (425+338+57)/2224 = 820/2224
f) Probability that a female passenger survived = 316/425
g) Probability that a child passenger survived = 57/109
h) Probability that a male passenger survived = 338/1690