An urn contains 15 red balls and 20 green balls. 8 balls are drawn randomly with

Question

An urn contains 15 red balls and 20 green balls. 8 balls are drawn randomly without replacement. Write down, with no arithmetic, Pr(x=k) for k = 0,1,2,3,4,5,6,7,8 if x= the number of red balls drawn.
Then, find the k-value such that Pr(x=k) is a maximum. Pr(x=k) greater than or equal to Pr(X= k+1) Pr(x=k) greater than or equal to Pr( X= k-1) An urn contains 15 red balls and 20 green balls. 8 balls are drawn randomly without replacement. Write down, with no arithmetic, Pr(x=k) for k = 0,1,2,3,4,5,6,7,8 if x= the number of red balls drawn.
Then, find the k-value such that Pr(x=k) is a maximum. Pr(x=k) greater than or equal to Pr(X= k+1) Pr(x=k) greater than or equal to Pr( X= k-1)
Then, find the k-value such that Pr(x=k) is a maximum. Pr(x=k) greater than or equal to Pr(X= k+1) Pr(x=k) greater than or equal to Pr( X= k-1)

Explanation / Answer

here the probability would be,

Pr(drawing 8 random balls) = 15cX * 20c8-X / 38c8 (where 'x' is the number of red balls drawn.)

the denominator remains constant.

so lets observe the numerator.

we know that 20cK is always bigger than 15cK.

so the will keep on increasing until (8-X) > X.

solution a. therefore the probability will be maximum when 15c3 * 20c5.

so at k = 3 probability(Pr) will be maximum.

solution b. same logic. At k = 3 probability(Pr) will be maximum and since k =4 probability starts decreasing.

solution c. same logic. At k = 3 probability(Pr) will be maximum and since k =4 and k=2 probability is less.

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