Question

1. you play a game that involves drawing two numbers from a hat. there are 25 pieces of paper numbered from 1 to 25 in the hat. each number is replaced after it is drawn. find the probability that you will draw the 3 on your first draw and a number greater than 10 on your second draw. (see example 3)

Explanation:

Step1: Probability of drawing 3

There are 25 numbers, so the probability of drawing 3 is $\frac{1}{25}$.

Step2: Probability of drawing >10

Numbers greater than 10 from 1 - 25 are 11 - 25, which is 15 numbers. So probability is $\frac{15}{25}=\frac{3}{5}$.

Step3: Multiply the probabilities

Since the draws are independent (with replacement), multiply the two probabilities: $\frac{1}{25} \times \frac{3}{5} = \frac{3}{125}$.

Answer:

$\frac{3}{125}$