Question

caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe. Two caps are drawn wothout replacement from the wardrobe. What is the probability that both of the caps are blue?

Answer 1

18/95

Explanation:

Probability Formula :

Probability (Event) = Number of outcomes with Event / Total outcomes

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Given :

⇒ 7 black caps

⇒ 4 yellow caps

⇒ 9 blue caps

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Solving :

P (1st cap is blue) :

⇒ Number of blue caps / Total caps

⇒ 9 / 7 + 4 + 9

⇒ 9/20

It mentions the cap is not replaced. Hence, when taking the probability of the 2nd cap, subtract a blue cap from the number of blue caps and the total.

P (2nd cap is blue) :

⇒ Number of blue caps - 1 / Total caps - 1

⇒ 9 - 1 / 20 - 1

⇒ 8/19

P (both caps are blue) :

⇒ P (1st cap blue) × P (2nd cap blue)

⇒ 9/20 × 8/19

⇒ 9/5 × 2/19

⇒ 18/95

Answer 2

18/95

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

For first draw

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

For second draw

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