Answer:
18/95
Step-by-step explanation:
What is probability?
Probability is simply the chances of something occuring.
As a formula, I like to say that formula = # of favorable outcomes / total # of outcomes
Where favorable outcomes is what we want to happen and total # of outcomes is the total number of possibilities.
In order to find the probability of the occurrence of something in a row, we multiply the individual probabilities of each action
Understanding the question
Here we are given that caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe and given this we want to find the probability of Caleb randomly selecting 2 blue caps without replacing it the first being drawn.
So here # of favorable outcomes = # of blue caps = 9
and
total number of outcomes = total # of caps = 7 + 4 + 9 = 20
Finding the probability
<em>For </em><em>first </em><em>draw</em>
First let's find the probability that caleb will select a blue cap the first time.
We know that probability = # of favorable outcomes / total # of outcomes
We also know that # of favorable outcomes = 9 and total # of outcomes = 20
Plugging this in, we get that the probability of Caleb randomly selecting a blue cap on the first draw is 9/20
<em>For </em><em>second </em><em>draw</em>
Because it says that caleb will not replace the cap when drawn it's important to subtract 1 from both the # of caps and # of blue caps
This results us in having # of favorable outcomes as 8 and total # of outcomes as 19
Plugging this in we get that the probability of Caleb drawing a blue cap the second time is 8/19
Finally to find the total probability of him selecting two blue caps in a row without replacing the first cap, we multiply the individual probabilities
From doing so we acquire 9/20 * 8/19 = 18/95
