Please this PROBABILITY question.

[X]

 A box contains 100 balls, of which r are red. Suppose that the balls are drawn from the box one at a time, at random, without replacement. Determine (a) the probability that the first ball drawn will be red; (b)the probability that the 50th ball drawn will be red; and(c)the probability that the last ball drawn will be red.


Thank you.

[Amit Goyal]

A box contains 100 balls, of which r are red. Suppose that the balls are drawn from the box one at a time, at random, without replacement. Determine (a) the probability that the first ball drawn will be red; (b)the probability that the 50th ball drawn will be red; and(c)the probability that the last ball drawn will be red.

(a) Pr (1st ball drawn will be red) = r/100
(b) Pr (50th ball drawn will be red) = r/100
(c) Pr (last ball drawn will be red) = r/100

Hint: Use symmetry

[Shreya Agrawal]

Thank you sir for helping me.

But I got the same answer from degroot solution manuel .

See sec. 1.7 prob. 10.

But I can't understand what it says.

Can you elaborate the reasoning behind this solution?
I will be obliged.

Thank you.

[Amit Goyal]

Hi Shreya,

This is what they mean to say:
We first list all possible sequences (or ways) in which 100 balls can be drawn where the ith term in the sequence is 1 if the  ith draw is red and 0 otherwise. And since draws are without replacement, we list all the sequences with exactly r  ones and (100 - r)  zeros. And all of them are equally likely. Thus,
Pr(there is 1 in the first spot of the sequence) = Pr(there is 1 in the 50th spot of the sequence) = Pr(there is 1 in the 100th spot of the sequence)  = r/100

[Shreya Agrawal]

Thanks a lot ,sir! My problem(or headache?) is now solved! You are great and caretaking teacher. Thank you.