3. Suppose that a box contains l l tickets, which are labeled respectively M , I

Question

3. Suppose that a box contains l l tickets, which are labeled respectively M , I , S , "S , I , S , S , I , "P", "P', "I". Three draws are made from this box at random, without replacement. a) (3 points) What is the chance that the same letter appears on all three draws? b) (2 points) What is the chance that the same letter does not appear on all three draws? c) (1 point) What is the chance that the letter "M" appears on the third draw? d) (1 point) Given that vowels appeared on the last two draws, what is the chance that the letter "M" appeared on the first draw?

Explanation / Answer

a)

Same letter appear on all 3 draws

(there are 4 (S,I), 2P and 1M)

Thus, required probability

P(S 3 times or I 3 times)

= 2*4/11*3/10*2/9

= 0.0485

b) P(Same letter does not appear on all 3 draws)

= 1 - P(Same letter appear on all 3 draws)

= 1 - 0.0485

= 0.9515

c)

P(M appears on 3rd draw)

= P(M does not appear on 1st and 2nd but appear on 3rd) as There is only 1 M

= 10/11*9/10*1/9

= 0.909

d)

P(M appears on 1st draw/vowels on next 2 draws)

2 vowels will reduce total characters from 11 to 9

and there is only 1M

Thus, required probability = 1/9

= 0.1111

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