Question

An urn contains 13 red marbles and 11 blue marbles. 12 marbles are chosen at random. What is the probability that 7 red marbles are chosen

Answer 1

The probability of selecting or choosing seven marbles is 0.29.

Let E be the event of choosing seven red marbles.

According to the given.

Total number of balls in an urn = 13 + 11 = 24

Total number of red marbles = 13

Total number of blue marbles = 12

Now, the total number of ways of selecting 12 marbles from 24 = $^{24} C_{12}$

And the number of ways of selecting 7 red marbles = $^{13} C_{7} \times ^{11} C_{5}$

As, we know that, the probability of any event can be calculated as by taking the ratio of favroble outcomes to the total number of outcomes.

Therefore, the probability of selecting or choosing seven marbles is given by

$P(E) = \frac{^{13}C_{7}\times\ ^{11} C_{5} }{^{24} C_{12} }$

⇒ P(E) = $\frac{\frac{13!\times11!}{7!\times6!\times 5!\times6! } }{\frac{24!}{12!12!} }$

⇒ P(E) =  792792/2704156

⇒P(E) = 0.29

Hence, the probability of selecting or choosing seven marbles is 0.29.

Find out more information about probability here:

brainly.com/question/11234923

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