Question

Suppose you have 60 red marbles and 40 blue marbles in a

box.If you pick 10 marbles without replacement, what is the
probabilityof selecting 6 red marbles?

Answer 1

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,

`n(S)=^(100)C_(10)=(100!)/(10!(100-10)!)=(100!)/(10!90!)=17310309456440,\\\\\\n(E)=^(60)C_6*^(40)C_4=(60!)/(6!54!)*(40!)/(4!36!)=50063860*91390.`

Therefore, the probability of event E is given by

`P(E)=(n(E))/(n(S))=(50063860*91390)/(17310309456440)=0.26.`

Thus, the required probability is 0.26.