Question

Find the indicated probability. a bag contains four chips of different colors, including red, blue, green, and yellow. a chip is selected at random from the bag and then replaced in the bag. a second chip is then selected at random. make a list of the possible outcomes (for example rb represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (hint: there are 16 possible outcomes.)

Answer 1

Answer:

0.25

Step-by-step explanation:

Let

r = red

b = blue

g = green

y = yellow

• If the first chip is r, the second can be r, b, g or y. The 4 possibilities are rr, rb, rg, ry.
• If the first chip is b, the second can be r, b, g or y. The 4 possibilities are br, bb, bg, by.

• If the first chip is g, the second can be r, b, g or y. The 4 possibilities are gr, gb, gg, gy.

• If the first chip is y, the second can be r, b, g or y. The 4 possibilities are yr, yb, yg, yy.

From the 4 + 4 + 4 + 4 = 16 possible outcomes, there are 4 in which the chips are of the same color (rr, bb, gg, yy).  The probability that the two chips selected are the same color is

4/16 = 0.25 = 25%

Answer 2

$\Omega=\{rr,bb,gg,yy,rb,rg,ry,bg,by,gy,yg,yb,gb,yr,gr,br\}\\ |\Omega|=16\\ A=\{rr,bb,gg,yy\}\\ |A|=4\\\\ P(A)=\dfrac{4}{16}=\dfrac{1}{4}=25\%$