Question

A bag of coins contains 6 quarters, 4 dimes, 5 nickels, and 7 pennies. Determine the probability of drawing a dime then a quarter, without replacement.

A. 12/231

B. 5/11

C. 6/121

D. 4/77

(There will most likely be more so if you want easy points just check)

Answer 1

i think the answer is B

Explanation:

Answer 2

Answer: The correct option is

(D)
`(4)/(77).`

Step-by-step explanation: Given that a bag of coins contains 6 quarters, 4 dimes, 5 nickels, and 7 pennies.

We are given to find the probability of drawing a dime then a quarter, without replacement.

Total number of coins = 6+4+5+7 = 22.

Let A represents the event of drawing a dime and B represents the event of drawing a quarter without replacement after drawing a dime.

Then, the probabilities of A and B are

`P(A)=\frac{\textup{number of dimes}}{\textup{total number of coins}}=(4)/(22)=(2)/(11)`

and

`P(B)=\frac{\textup{total number of quarters}}{\textup{total number of coins left after drawing a dime}}=(6)/(21)=(2)/(7).`

Therefore, the probability of drawing a dime then a quarter, without replacement is given by

`P(A\cap B)\\\\=P(A)* P(B)~~~~~~~~~~~~~~~~~~~[\textup{since A and B are independent events}]\\\\\\=(2)/(11)*(2)/(7)\\\\\\=(4)/(77).`

Thus, the required probability is
`(4)/(77).`

Option (D) is CORRECT.