4) A bag of marbles contains: 6 red marbles 4 bhue maebles 2 nge are taken from

Question

4) A bag of marbles contains: 6 red marbles 4 bhue maebles 2 nge are taken from the bag with whas baur o marbles are taken from the bag with splcwhas w I t are blue? 3 green marbles replaceest, what is the peobability that both marbiles are blue bles ae taken from the bag without mplacenerat, wlhat is the probablity that both marbles are blue? e If two marbles are taken from the bag withbout replacement, what is the probability that the fi marble was orange and the second marble is red? 5) For the following, ignore leap years and assume that births on the 365 different days of the y qually likely a) What is the probability that a randomly selected person was born on May 7th?

Explanation / Answer

6 red, 4 blue, 2 orange, 3 green Total marble = 15

a) 2 marbles can be drawn from 15 marbles with replacements in 15*15 ways
In 1st pick a blue marble can be drawn in 4 ways, in second pick also it can be drawn in 4 ways as replacements are allowed. Total in 4*4 = 16 ways
Probability = 16/15*15 = 16/225

b) 2 marbles can be drawn from 15 marbles without replacements in 15P2 ways
2 blue marbles can be drawn from 4 blue in 4P2 ways
Probability= 4P2/ 15P2 = 12/210 = 2/35

c) 2 marbles can be drawn from 15 marbles without replacements in 15P2 ways
In 1st pick 1 orange can be picked in 2 ways, in second pick 1 red can be picked in 6 ways. Total 6*2 = 12 ways
Probability = 12/ 15P2 = 12/210 = 2/35

5.a) Probability of a randomly selected person born on 7th May = 1/365

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