A bag contains 17 marbles: 10 purple and 7 green. The purple marbles are numbere

Question

A bag contains 17 marbles: 10 purple and 7 green. The purple marbles are numbered 1 through 10 and the green ones are numbered 11 through 17. If one marble is chosen, what is the probability that it is purple? If one marble is chosen, what is the probability that it is green? If one marble is chosen, what is the probability that it is both purple and even? If one marble is chosen, what is the probability that it is NOT both purple and even? If one marble is chosen, what is the probability that it is green or even? If one marble is chosen, what is the probability it is even, given that it is green? If two marble are chosen with replacement, what is the probability both are odd? If two marble are chosen without replacement what is the probability that the first is purple and the second is green? Give an example of two events that are mutually exclusive when one marble is chosen. If 89 marbles are chosen at random without replacement, what is the probability that at least one is purple?

Explanation / Answer

1) probability of purple marble = 10/17

2) probability of green marble =7/17

3)probability of purple marble and even both is 5/10 as purple are numbered 1 to 10 so there are 5 even numbers in them .5/17

4)not purple not even means it is green and odd = 4/17 as 11 ,13,15,17 are green and odd.

5)given that it is green and is even = 5/17×3/17 = 15/289 . As probability of even green marbles is 3/17.

6)probability of both marbles odd is 9/17 × 9/17 = 81/289

7) probabiltiy of first marble purple is 10/17 and second marble green is 7/16 .

So total probability is 10/17 × 7/16 = 70/ 272

8)example of mutually exclusive is selecting 2 green and 5 purple marbles with replacement .

Bonus : total marbles to be selected is 8 , thus total outcomes are 17C8 i.e combination .

Atleast one purple implies 10C1×7C7 + 10C2×7C6 + 10C3×7C5 + 10C4×7C4 + 10C5 × 7C3 + 10C6 × 7C2 + 10C7 × 7C1 + 10C8 × 7C 0

This whole divided by 17C8

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