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zvonat [6]
3 years ago
14

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

Mathematics
1 answer:
andrew-mc [135]3 years ago
6 0

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}=\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.

Therefore, the probability of event E is given by

P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.

Thus, the required probability is 0.26.

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