Question

A box contains five slips of paper, each with one of the letters A, B, C, D, or E written on it. Another box has four slips of paper, each with one of the numbers 1, 2, 3, or 4 written on it. Without looking, Nancy draws a slip of paper from each box. What is the probability that Nancy draws the letter B from one box and the number 2 from the other box?

Answer 1

20% chance for the letter box and 25% chance for Number box.

Answer 2

Answer:

The probability that Nancy draws the letter B from one box and the number 2 from the other box is:

$\dfrac{1}{20}$

Step-by-step explanation:

We know that the probability of drawing a slip of paper from one box is independent of drawing a piece of slip from the other.

Let first box contain five slips of paper, each with one of the letters A, B, C, D, or E written on it.

This means that the probability of drawing B is:

ratio of the number of slips containing B to the total number of slips.

i.e.

$P(Drawing\ B)=\dfrac{1}{5}$

Second box has four slips of paper, each with one of the numbers 1, 2, 3, or 4 written on it.

This means that the probability of drawing number 2 is:

ratio of the number of slips containing number 2 to the total number of slips.

i.e.

$P(Drawing\ 2)=\dfrac{1}{4}$

Hence,

$P(drawing\ B\ and\ number\ 2)=P(drawing\ B)\times P(drawing\ 2)\\\\i.e.\\P(drawing\ B\ and\ number\ 2)=\dfrac{1}{5}\times \dfrac{1}{4}\\\\P(drawing\ B\ and\ number\ 2)=\dfrac{1}{20}$

Hence, the probability is:

$\dfrac{1}{20}$