A box contains 5 plain pencils and 5 pens. A second box contains 3 color pencils and 7 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.
Disagree with the bot's answer
The order in which they are picked is not specified.
prob(your event) = prob(pen, then crayon) + prob(crayon, then pen)
= (5/10)(3/10) + (3/10)(5/10)
= 30/100
= 3/10
The probability of selecting a plain pencil from the first box is 5/10, which can be simplified to 1/2. The probability of selecting a color pencil from the second box is 3/10.
To find the probability of both events happening, we need to multiply the probabilities:
1/2 * 3/10 = 3/20
Therefore, the probability of selecting a plain pencil from the first box and a color pencil from the second box is 3/20.