Sara’s little brother is getting ready to color the picture of a rainbow that Sara drew for him. To make the task easier for her
brother, Sara picks out crayons that match the colors of the rainbow and places them in a box. She asks her brother to randomly pick two crayons from the box, one after the other. The probability that the first color is violet and the second is orange, if the first crayon is replaced, is . The probability that the first color is violet and the second is orange, if the first crayon is not replaced, is .
There are seven colors in a rainbow, namely red, orange, yellow, green, blue, indigo and violet. Therefore, there are 7 total possibilities. Keep in mind that when we two events are to happen together, their probabilities are mulitplied. Therefore, in the first case, P(violet) = 1/7 and P(orange) = 1/7; P(violet then orange) = 1/7 * 1/7 = 1/49. If the crayon is not replaced, P(orange) = 1/6. Therefore, P(violet then orange) = 1/7 * 1/6 = 1/42.
Sample response: Factor the GCF of five out of the total bill. Divide both terms of the expression by 5. The result is 5x – 23, which is the expression that can be used to find the amount each person pays.
