Question

Box 1 (has 2 c balls and 3 w balls); Box 2 (has 4 c balls and 2 w balls)
5. Following are two boxes containing colored and white balls. A ball is drawn at random from box 1. Then a ball is drawn at random from box 2, and the colors of balls from both boxes are recorded in order.

Find each of the following:
a. The probability of two white balls
b. The probability of at least one colored ball
c. The probability of at most one colored ball
d. The probability of (black circle and white circle) or (white circle and black circle)

Answer 1

a) two white balls first box has 5 balls , 3 are white , probability is
\[\frac{3}{5}\] for a white one. second box has 6 ball, two white, so probablity of the secdond being white is
\[\frac{2}{6}=\frac{1}{3}\] probability first one is white AND second one is white is
\[\frac{3}{5}\times \frac{1}{3}=\frac{1}{5}\]

Answer 2

at least one colored ball means they are not both white. so it is
\[1-\frac{1}{5}=\frac{4}{5}\]

Answer 3

Oh ok that makes a better difference than what the book explained

Answer 4

we can do the third one too, but it is longer.

Answer 5

I am learning so its okay

Answer 6

at most one colored ball means
both are white (we have that one) OR
first is white and second is colored OR
first is colored and second is white

Answer 7

first is white AND second is colored we have
\[\frac{3}{5}\times \frac{4}{6}=\frac{2}{5}\]

Answer 8

first one is colored AND second one is white is
\[\frac{2}{5}\times \frac{2}{6}=\frac{2}{15}\]

Answer 9

Ok starting to make more sense

Answer 10

so now we add them up and get
\[\frac{1}{5}+\frac{2}{5}+\frac{2}{15}\] whatever that is

Answer 11

i hope you got the hint that when i wrote AND we multiply and OR we added

Answer 12

yes i understand the math terminology

Answer 13

good luck!

Answer 14

Thank you very much