Question

50 pencils are in a box. 8 of them are mechanical. what is the probability of drawing 2 mechanical pencils if the first one is placed back in the box before the second draw? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate probability of first draw

The probability of drawing a mechanical pencil on the first draw is the number of mechanical pencils divided by the total number of pencils. So $P_1=\frac{8}{50}= 0.16$.

Step2: Calculate probability of second draw

Since the first pencil is replaced, the probability of drawing a mechanical pencil on the second draw is the same as the first draw. So $P_2=\frac{8}{50}=0.16$.

Step3: Calculate joint - probability

For independent events (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=0.16\times0.16 = 0.0256\approx0.03$.

Answer:

$0.03$