Question

There are 4 white marbles,6 red marbles,and 2 blue marbles.Once a marble is selected,it is not replaced.Find the probability of selecting 2 blue marbles.

Answer 1

Answer:

There are 4 white marbles,6 red marbles, and 2 blue marbles. Once a marble is selected,it is not replaced.Find the probability of selecting 2 blue marbles. --- # of ways to succeed: 2C2 = 1 --- # of random pairs: 12C2 = 66 --- P (2 blue) = 1/66

Answer 2

Answer:

$\dfrac{1}{66} \approx 1.5\%$

Step-by-step explanation:

Probability is a measure of the likelihood or chance that a specific event or outcome will occur.

$\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}$

We are told that there are 4 white marbles, 6 red marbles and 2 blue marbles. Therefore, the probability of selecting a blue marble on the first pick is:

$\sf P(blue\;1st)=\dfrac{2}{4+6+2}=\dfrac{2}{12}=\dfrac{1}{6}$

As the first marble selected is not replaced, we now have 1 blue marble remaining, and a total of 11 marbles remaining.

Therefore, the probability of selecting a blue marble on the second pick is:

$\sf P(blue\;2nd)=\dfrac{1}{11}$

To calculate the probability of both events occurring (selecting 2 blue marbles), we multiply the probabilities:

$\sf P(blue\;1st)\;and\;P(blue\;2nd)=\dfrac{1}{6} \times \dfrac{1}{11}=\dfrac{1}{66}$

Therefore, the probability of selecting 2 blue marbles without replacement is 1/66 ≈ 1.5%.