There are an arbitrary number of balls in a bag. Each individual ball has a numb

Question

There are an arbitrary number of balls in a bag. Each individual ball has a number written on them of either "1" or "2". You are given that the probability of picking a ball with the number "2" written on it is 0.6. You start to pick an individual ball out of the bag each time.

(i) What is the probability that the first 10 balls picked, that 6 balls have the number "2" written on them?

(ii) What is the probability that out of the first 10 balls, that at least 2 balls have the number "1" written on them?

(iii) If you stop picking balls out of the bag after you have found 6 balls with the number "2" written on them, what is the probability that you will stop after having picked exactly 10 balls?

Explanation / Answer

(i)

the probability that the first 10 balls picked, that 6 balls have the number "2" written on them = 6/10 = 0.6

(ii)

the probability that out of the first 10 balls, that at least 2 balls have the number "1" written on them

=1/10=0.1

the probability that you will stop after having picked exactly 10 balls= 1/2 =0.5

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