A theater keeps a drum full of 3D glasses infront of the theater- As each patron

Question

A theater keeps a drum full of 3D glasses infront of the theater- As each patron enters, a glass is randomly picked and given to him/her and they give it back as they leave. The drum has to 40 and 60 blue glasses. John is the first in line and loved the show so he went back latter in the day. (A) What is the likehood that he got a red 3D glasses on both occasions Calculate (B)What is the likelihood that he got a red glass on the first day and a blue on the second day. Calculate (C) Would answer in a and b different if John found himself to be third in line on the second day. explain.

Explanation / Answer

a) We have a total of 100 glasses 40 red and 60 blue

The probability of a red glass =40/100=0.4

The probability of a blue glass =60/100=0.6

If John is first in line then he has the likelihood of getting any glasses from 100

Therefore

Probability of getting a red glass on the first occasion =0.4

Probability of getting a red glass on the second occasion =0.4

Probability of getting a red glass on both occasions =0.4*0.4=0.16

b) Probability of getting a red glass on the first occasion =0.4

Probability of getting a blue glass on the second occasion =0.6

Likelihood that he got a red glass on the first day and blue glass on th second day=0.4*0.6=0.24

c) Now the person is third in line ie, 2 people have taken 2 glasses so there are only 98 glasses from which he can get his glasses

For bit (a) the probability is (40/98)*(40/98)=0.17 (rounded to 2 decimal places)

For bit (b) the probability is (40/98)*(60/98)=0.25 (rounded to 2 decimal places)

So the answers of both the above bits a and b will be different.

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