Question

A box contains 3 red marbles, 6 blue marbles, and 1 white marble. the marbles are selected at random, one at a time, and are not replaced. find the probability. p(red and red and red)

Answer 1

let's work this step by step. There are a total of 10 marbles in the box. The chance of getting a red marble on the first pick can be calculated like this.

Total number of red marvels / Total number of marble s
3/10 = 0.333

Multiply it by 100 to put the answer in percent

0.333*100 = 33.3%

33.3% chance of getting red marble at the first try.

Next since we can't replace the marvel back into the box now we have a total number of 9 marvels and 2 red marbles ( 2 red marbles , 6 blue marble s and 1 white marble )
Total number of red marbles / Total number of marbles
2/9 = 0.22
then multiply by 100
0.22*100 = 22.2%

22.2% chance of getting red marble at the second try.

Now there is only one red marble and a total of 8 marbles(1 red marble 6 blue marbles and 1 white marble)
Total number of red marbles / Total number of marbles
1/8 = 0.125
then multiply by 100
0.125*100 = 12.5%

12.5% chance of picking red marble at the third try.
all together p(33.3% , 22.2% , 12.5%)

Answer 2

The probability helps us to know the chances of an event occurring. The probability of selecting red and red and red marble is 0.1667.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

The box contains 3 red marbles, 6 blue marbles, and 1 white marble. Therefore, the total number of marbles is 10. Now, the probability of selecting a red marble can be written as,

$\rm Probability=\dfrac{6}{10}$

Now, since the marble is not kept back the number of red marbles is 5, while the number of total marbles is 9.

$\rm Probability=\dfrac{5}{9}$

Further, the marble is not kept back the number of red marbles is 4, while the number of total marbles is 8.

$\rm Probability=\dfrac{4}{8}$

Thus, the probability of selecting red and red and red marble can be written as,

$\text{P(red and red and red)}=\dfrac{6}{10} \times \dfrac{5}{9} \times \dfrac{4}{8} =\dfrac{120}{720}=0.1667$

Hence, the probability of selecting red and red and red marble is 0.1667.

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