The probability that a professor in the business department is full time is [tex]30[/tex]%. If we randomly select [tex]9[/tex] professors; the probability that [tex]3[/tex] or fewer of them are FULL TIME is [tex]10[/tex]%
How can find the probability of full time ?
Probability of selecting [tex]3[/tex] from [tex]9[/tex]people = [tex]3/9[/tex]
Probability of selecting [tex]2[/tex] people= [tex]2/9[/tex]
Probability of selecting [tex]1[/tex] people=[tex]1/9[/tex].
Probability of selecting up to to 3 people is [tex]1/9+2/9+3/9 = 6/9[/tex].
Every person who got selected is full time person has probability [tex]0.3[/tex]
=> For selection of people up to [tex]3[/tex] is
[tex]=\frac{3}{9} *0.3\\=0.1\\[/tex]
[tex]=10[/tex]%
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