Question

A box contains three plain pencils and 5 pens. A second box contains three colored pencils and three crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon form the second box are selected?

Answer 1

Answer:

Therefore the probability that a pen from the first box and a crayon from the second box are selected is $\frac5{16}$

Step-by-step explanation:

Probability:

The ratio of the number of favorable outcomes to the number all possible outcomes of the event.

$Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}$

Given that,

Three plain pencils and 5 pens are contained by the first box.

Total number of pens and pencils is =(3+5)=8

The probability that a pen is selected from the first box is

=P(A)

$=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}$

$=\frac{5}{8}$

A second box contains three colored pencils and three crayons.

Total number of pencils and crayons is =(3+3)=6

The probability that a crayon is selected from the second box is

=P(B)

$=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}$

$=\frac{3}{6}$

Since both events are mutually independent.

The required probability is multiple of the events

Therefore the required probability is

$=\frac58\times \frac36$

$=\frac5{16}$