What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?

Question

A box contains 5 plain pencils and 5 pens. A second box contains 7 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?

Write your answer as a fraction in simplest form.

Answer 1

Probability of plain pencil from first box =1/(5+5) = 1/10 =P1

Probability of color pencil from second box =1/(3+7) = 1/10 =P2

Probability of both the event independent of each other = P_1*P₂₌ 1/100

Answer 2

FINAL ANSWER:

The probability is 7/20

Probability is how many possible DESIRED outcomes there are DIVIDED BY the TOTAL possible outcomes.

When it comes to combining the probability of more than one event, I use a "hint" that finding the probability of one OR the other usually involves ADDING individual probabilities; and finding the probability of one AND the other, usually involves MULTIPLYING individual probabilities.

I am interpreting the problem as:

Finding the probability that BOTH

a plain pencil is picked out of one box

AND

a colored pencil is picked out of the other box.

The probability of picking 1 plain pencil out of a box containing 5 plain pencils and 5 pens is

{5 possible DESIRED plain pencils} out of {the TOTAL possible 5 plain pencils PLUS 5 pens},

or 5 chances out of 5+5=10,

which is 5/10=1/2.

The probability of picking 1 color pencil out of a box containing 7 color pencils and 3 crayons is

{7 possible DESIRED color pencils} out of {the TOTAL possible 7 color pencils PLUS 3 crayons}

or 7 chances out of 7+3=10.

which is 7/10.

Since we are looking for the probability of picking 1 plain pencil out of one box AND 1 colored pencil out of the other box, we multiply probabilities.

(1/2)(7/10)=7/20

FINAL ANSWER:

The probability is 7/20