Answer:
Step-by-step explanation:
It is given that A jar contains ten black buttons and six Brown buttons.
Therefore, total number of buttons= 16.
Then, the probability of getting black button will be=[tex]\frac{10}{16}=\frac{5}{8}[/tex] and the probability of getting brown button=[tex]\frac{6}{16}=\frac{3}{8}[/tex].
It is given that 9 buttons are picked at random and We have to find he probability that exactly five of them are black. Since, it is the case of the random variables, therefore the probability that exactly five of them are black=[tex]9C_{5}{\times}(\frac{5}{8})^{5}{\times}(\frac{3}{8})^{4}[/tex]
=[tex]\frac{9!}{5!4!}{\times}\frac{5^53^4}{8^9}[/tex]
=[tex]\frac{(5^5)(3^6)(14)}{8^9}[/tex]
Thus,probability that exactly five of them are black=[tex]\frac{(5^5)(3^6)(14)}{8^9}[/tex].
