Probability for minimum and maximum

Probability Level 3

Three numbers are chosen at random without replacement from {1, 2, 3....8}. Given that the maximum is 6, the probability that the minimum is 3 is p q \frac{p}{q} where p p and q q are positive coprime integers. What is the value of p + q p + q ?


The answer is 6.

Arpit Dhimanj by Arpit Dhimanj , 23, India

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3 solutions

Upamanyu Singh
Jul 7, 2014

Maximum is 6 Therefore other two numbers can be chosen out of 1,2,3,4,5 in 5C2=10 ways

Max-6 & min-3 then the third number can be 4 or 5(2 cases)

Therefore probability is 2/10 or 1/5

Thus p+q=6

8 Helpful 0 Interesting 0 Brilliant 0 Confused

6 is chosen as the maximum. Which means the minimum can only be lesser than 6. That leaves us with 1,2,3,4,5 to be chosen as the minimum. 3 can be chosen out of them in only one way. And there are 5 different ways to choose a minimum. therefore probability that 3 will be chosen is 1/5. p+q=6. EASY PEASY!!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Priya Narang
Jul 7, 2014

Choosing 1 as smallest cases are 4
choosing 2 as smallest - 4 Choosing 3 as smallest 4 Chossing 4 as smallest 3 choosing 5 as smallest 3 Choosing 3 as not smallest 2 (326,316) P= 4 q= 20

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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