Question

A paper grocery bag has 6 lemons, 3 limes, and 4 oranges. For each question, you willremove fruit from the bag without looking, one at a time.Find the answer to the question, and type your answer into the box as a decimalrounded to the nearest thousandth.What is the probability of removing a lemon, then a lime, with replacement?

Answer 1

$\text{probability}=\frac{\text{ number of favorable outcomes}}{\text{ total number of outcomes}}$

The probability of removing a lemon is:

$p_1=\frac{6}{6+3+4}=\frac{6}{13}$

The probability of removing a lime is:

$p_2=\frac{3}{6+3+4}=\frac{3}{13}$

The events: removing a lemon, then a lime, with replacement, are independent, then the probability that one event happens after the other one is:

$p_1\cdot p_2=\frac{6}{13}\cdot\frac{3}{13}=\frac{18}{169}_{}=0.107$