Question

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____ .

options for the first one is:
1/7
2/7
1/21
1/42
1/49
options for the second one is:
1/7
2/7
1/21
1/42
1/49
i do not know how to figure this out!!! Please help me!

Answer 1

1 49 and 1 42 is the most probable outcome

Answer 2

If the crayons are replaced after they are drawn, the probability of drawing any particular color is 1/7.Also the result of each draw is independent of any previous result. Therefore the solution to the first part of the question is found from:
`P(violet\ then\ orange)=(1)/(7)*(1)/(7)=(1)/(49)`

If the crayons are not replaced after they are drawn, the probability of drawing violet on the first pick is 1/7. Then there are only six crayons left, so the probability of drawing orange is 1/6. The solution to the second part of the question is found from:

`P(violet\ then\ orange)=(1)/(7)*(1)/(6)=(1)/(42)`