What is the probability that you will get admission in atleast two colleges?

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Solution

Given
$P (X, x) = ⎧ ⎨ ⎩ \begin{matrix} K x, i f x = 0 o r 1 2 K x, i f x = 2 K [5 - x], i f x = 3 o r 4 \end{matrix}$
Possibility for atleast $2$ colleges
$= P (X = 2) + P (X = 3) + P (X = 4) = 2 K x + K [5 - x] + K [5 - x] = 2 K x + 5 K - K x + 5 K - K x = 10 K$

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Q. Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that
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What is the probability that you will get admission in atleast two colleges?

GivenP(X,x)=⎧⎨⎩Kx,ifx=0or12Kx,ifx=2K[5−x],ifx=3or4Possibility for atleast 2 colleges=P(X=2)+P(X=3)+P(X=4)=2Kx+K[5−x]+K[5−x]=2Kx+5K−Kx+5K−Kx=10K

Given
$P (X, x) = ⎧ ⎨ ⎩ \begin{matrix} K x, i f x = 0 o r 1 2 K x, i f x = 2 K [5 - x], i f x = 3 o r 4 \end{matrix}$
Possibility for atleast $2$ colleges
$= P (X = 2) + P (X = 3) + P (X = 4) = 2 K x + K [5 - x] + K [5 - x] = 2 K x + 5 K - K x + 5 K - K x = 10 K$