Answer: The required probability is 0.26.
Step-by-step explanation: Given that there are 60 red marbles and 40 blue marbles in a box 10 marbles are picked without replacement.
We are to find the probability of selecting 6 red marbles.
Since the marbles are picked up without replacement, so it is a situation of combination.
Let S denote the sample space of the experiment of drawing 10 marbles and E denote the event that 6 marbles are red.
So,
[tex]n(S)=^{100}C_{10}=\dfrac{100!}{10!(100-10)!}=\dfrac{100!}{10!90!}=17310309456440,\\\\\\n(E)=^{60}C_6\times^{40}C_4=\dfrac{60!}{6!54!}\times\dfrac{40!}{4!36!}=50063860\times91390.[/tex]
Therefore, the probability of event E is given by
[tex]P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.[/tex]
Thus, the required probability is 0.26.
