Question

A chef draws cookies randomly from a box containing 6 cookies of the same shape and size. There is 1 chocolate cookie, 3 almond cookies, and 2 butter cookies. He draws 1 cookie and then draws another cookie without replacing the first one. Find the probability of picking 1 almond cookie followed by another almond cookie. Show ALL your work AND write your answer as a fraction, decimal, and percent.

Answer 1

The probability of picking 2 almond cookies without replacing it is 1/5

Step-by-step explanation

Given that

The total number of cookies in the box is 6

The number of chocolate cookie is 1

The number of almond cookies is 3

The number of butter cookies is 2

Probability is defined as likelihood of an event to happen

`\text{ Probability }=\text{ }\frac{\text{ possible outcomes}}{\text{ total outcomes}}`

Recall, that the condition given is without replacement

So, probability of picking 1 almond cookie first is

`\text{ P\lparen1st almond cookie\rparen}=\text{ }(3)/(6)`

Since, the first almond cookie picked was not replaced, then, the total number of cookies in the box will be 5 and also, the number of almond cookies will be 2

hence, the probability of picking the second almond is

`\text{ P\lparen2nd almond cookie\rparen }=\text{ }(2)/(5)`
`\begin{gathered} \text{ P\lparen2 almond cookies\rparen }=\text{ }(3)/(6)*(2)/(5) \\ \text{ P\lparen2 almond cookies\rparen }=(6)/(30) \\ \text{ P\lparen2 almond cookies\rparen }(1)/(5) \end{gathered}`

Therefore, the probability of picking 2 almond cookies without replacing it is 1/5