Probability 2 Question 10

10. Three numbers are chosen at random without replacement from 1,2,,10. The probability that the minimum of the chosen number is 3 , or their maximum is 7 , is … .

(1997C, 2M)

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Answer:

Correct Answer: 10. 13.9

Solution:

  1. Let E1 be the event getting minimum number 3 and E2 be the event getting maximum number 7 .

Then, P(E1)=P (getting one number 3 and other two

=1C1×7C210C3=740

from numbers 4 to 10)

P(E2)=P (getting one number 7 and other two from

=1C1×6C210C3=18

numbers 1 to 6 )

and P(E1E2)=P( getting one number 3 , second number 7 and third from 4 to 6 )

=1C1×1C1×3C110C3=140P(E1E2)=P(E1)+P(E2)P(E1E2)=740+18140=1140



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