Question

A box has 5 beads of the same size, but all are different colors. Tina draws a bead randomly from the box, notes its color, and then puts the bead back in the box. She repeats this 3 times. What is the probability that Tina would pick a red bead on the first draw, then a green bead, and finally a red bead again?

Answer 1

`(1)/(25)`

Explanation:

To solve this problem we have the standard definition of a probability, that is:

`P=(n\° cases)/(n\° total events)`

So, we have to identify how many cases are about the probability that it's being asked, and then we divide it by the total number of events possible.

In this case, each bead has the same probability of being picked, that is,
`(1)/(5)`, because we have 5 beads in total, and only one of each color. So, all beads have
`(1)/(5)` of probability to be selected.

In addition, Tina wants to reproduce the experiment three times, where she puts back each bead after being picked, this means that each events is independent, that is, each bead doesn't influence the probability of others. When events are independent, this is shown as a multiplication, so basically we have to multiply three times the same fraction.

`P = (1)/(5) (1)/(5) (1)/(5) = (1)/(125)`

Therefore, the probability of picking first a red bead, second a green one and third a red one agains, is
`(1)/(125)`, which is a pretty low chance, it's hard to happen.

Answer 2

probability of picking red on first draw = 1/5
but then the bead is put back
probability of picking green = 1/5
but then the bead is put back
probability of picking red again = 1/5

1/5 * 1/5 * 1/5 = 1/125 <===