I play a light game with my daughter. We have a small hand-held projector that d

Question

I play a light game with my daughter. We have a small hand-held projector that displays an image the ceiling from a small interchangeable plastic insert. You cannot tell the image on the insert until you project it on the ceiling. There are three inserts with three unique pictures: Elsa, Anna, and Olaf We randomly pick one and guess before projecting the answer. Each time we replace the insert and repeat the experiment three times. What is the probability of at least one correct guess in three attempts?

Explanation / Answer

Solution:

   We are given that: There are three inserts with three unique pictures: Elsa, Anna, and Olaf.
We have to randomly pick one and guess and replace it.

We have three attempts. So the probability of any correct guess = 1 / 3 then

the probability of incorrect guess = 1 - 1/3 = 2/3

We have to find the probability that: at least one correct guess in three attempts.

Thus

P( At least one correct guess) = ..........?

P( At least one correct guess) = 1 - P( No one correct guess)

P( At least one correct guess) = 1 - P( All three are an Incorrect guess)

P( At least one correct guess) = 1 - ( 2 / 3 )3

P( At least one correct guess) = 1 -   ( 0.6667)3

P( At least one correct guess) = 1 -   0.2963

Thus correct option is First option: 1 - 0.2963

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