Question

Q1. Consider a pot containing balls. Each ball has a number painted on it with the number ranging from 1 to 9. For 1<=n<=9 there are n balls with the number n painted on it. For each number i where i lies between 1 and 9, write down the probability that a ball drawn at random from the pot has the number i painted on it.

Q2) Put 3 balls into 3 boxes randomly. Find 1) Probability that there is just one ball in each box. 2) The Probability that there is one empty box

Answer 1

According to the problem :-

Number of balls with number 1 painted on it = 1

Number of balls with number 2 painted on it = 2

Number of balls with number 3 painted on it = 3

Number of balls with number 4 painted on it = 4

Number of balls with number 5 painted on it = 5

Number of balls with number 6 painted on it = 6

Number of balls with number 7 painted on it = 7

Number of balls with number 8 painted on it = 8

Number of balls with number 9 painted on it = 9

So total number of balls = 1+2+3+4+5+6+7+8+9 = 45

Probability that a ball drawn at random from the pot has the number 1 painted on it = 1/45

Probability that a ball drawn at random from the pot has the number 2 painted on it = 2/45

Probability that a ball drawn at random from the pot has the number 3 painted on it = 3/45 = 1/15

Probability that a ball drawn at random from the pot has the number 4 painted on it = 4/45

Probability that a ball drawn at random from the pot has the number 5 painted on it = 5/45 = 1/9

Probability that a ball drawn at random from the pot has the number 6 painted on it = 6/45 = 2/15

Probability that a ball drawn at random from the pot has the number 7 painted on it = 7/45

Probability that a ball drawn at random from the pot has the number 8 painted on it = 8/45

Probability that a ball drawn at random from the pot has the number 9 painted on it = 9/45 = 1/5

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