Suppose that roughly 40 of all videos on the internet is a c

Suppose that roughly 40% of all videos on the internet is a cat video and you decide to click on videos at random.

a.) Declare a random variable representing the number of cat videos we can watch before clicking on a non-cat video and provide the expected number of cat videos as well as the variance.

b.) Find the probability that we watch 6 cat videos in a row before the first dog video.

c.) Find the probability that we watch at least 3 cat videos before the first non-cat video.

d.) Declare a random variable that represents the number of cat videos we can watch before seeing the 4th non-cat video and provide the expected value as well as the variance. (Use a different letter as above.)

e.) Find the probability that we watch 7 cat videos before the 4th non-cat video.

Solution

40% of all videos is cat video.

a) Let X - no of cat videos before we watch non cat video

X can take values as 0 1 2 ...     r

P(X) 0.60 0.40(0.6) (0.4)^2(0.6) ... (0.4)r(0.6) ..

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b) P(X>=6) = 1-P(x=1,2,3,4,5)

=  1- 0.6-0.24-0.096 -0.0384-0.01536

=0.01024

c) P(X>=3) = 1-P(x=0,1,2)

= 1- 0.6-0.24-0.096 = 1-0.936 = 0.064

e) P(X>=7) = 0.01024-P(X=7) = 0.01024-0.006144=0.004096