Question

GiGi is making a necklace with a bag of 50 beads (10 red, 25 white, 5 yellow, and 8 blue, and 2 green) find the probability the first 5 beadz of the necklace to be white, yellow, green, white, and red (consecutively). Independent or Dependent

Answer 1

When Gigi is making the necklace, she take one bead from the bag at the time to make it.

In this scenario, there is no reposition, which means that each time she take one bead out of the bag, the total number of beads and the number of beads of the color chosen is modified.

For example, at first, there are:

Total: 50 beads

Red: 10

White: 25

Yellow: 5

Blue: 8

The probability of the first bead being white can be determined as follows:

`P(W_1)=(25)/(50)`

For the next bead, the total number would have decreased to 49, and the number of white beads on the bag would be 24.

So the probability of the second bead is modified:

"the second bead is yellow"

`P(Y_2)=(5)/(49)`

Because the number of beads on the bag is decreased.

Following the definition of independent events, since the probability of the choosing, the next bead is modified by the previous one, you can say that the colors of the beads are dependent.

To determine the probability of the first 5 beads being: white, yellow, green, white, and red (consecutively) can be determined as:

`\begin{gathered} P(W_1\cap Y_2\cap G_3\cap W_4\cap R_5)=P(W_1)\cdot P(Y_2)\cdot P(G_3)\cdot P(W_4)\cdot P(R_5) \\ (25)/(50)\cdot(5)/(49)\cdot(2)/(48)\cdot(24)/(47)\cdot(10)/(46)=(25)/(105938)\approx0.0002 \end{gathered}`