2 Answers

Riddik · Answer 1 · 2021-09-03T05:56:37+0000

Answer:

(5)/(273)

They are dependent events.

Explanation:

Given:

Number of $1 gift certificates = 2

Number of $2 gift certificates = 2

Number of $3 gift certificates = 10

To find:

Probability that a $1 gift certificate is selected, then a $3 and then a $2 certificate is selected = ?

Solution:

First of all, let us learn about the formula of probability of any event E:

$P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Finding probability of choosing $1 gift certificate in the first turn:

Number of favorable cases or number of $1 gift certificates = 2

Total number of cases or total number gift certificates = 2 + 2 + 10 = 14

So, required probability =
$(2)/(14) \Rightarrow (1)/(7)$

Finding probability of choosing $3 gift certificate in the 2nd turn:

Number of favorable cases or number of $1 gift certificates = 10

Now, one gift certificate is already chosen,

So, Total number of cases or total number gift certificates = 14 - 1 = 13

So, required probability =
(10)/(13)

Finding probability of choosing $2 gift certificate in the 3rd turn:

Number of favorable cases or number of $2 gift certificates = 2

Now, two gift certificates is already chosen,

So, Total number of cases or total number gift certificates = 14 - 2 = 12

So, required probability =
$(2)/(12) \Rightarrow (1)/(6)$

Probability that a $1 gift certificate is selected, then a $3 and then a $2 certificate is selected:

$(1)/(7)* (10)/(13)* (1)/(6)\\\Rightarrow (5)/(273)$

They are dependent events because total number of cases and total number of favorable cases depend on the previous chosen gift certificate.

So, the answer is:

(5)/(273)

They are dependent events.

Please log in or register to add a comment.