Question

A wallet contains 4 dimes, 5 pennies, and 7 nickels. Event A is defined as drawing a dime on the first draw and event B is defined as drawing a nickel on the second draw.

If Lee draws two coins from the wallet, one after the other without replacement, what is P(B|A) expressed in simplest form?

A.) 1/4
B.) 6/15
C.) 7/16
D.) 7/15

Answer 1

A.) ¼

Explanation:

There are two coins being drawn from the wallet every time:

Two dimes → Event A

Two nickels → Event B

Out of the total of 16 coins

`(1)/(4) = (4)/(16)`

I hope this is correct, and as always, I am joyous to assist anyone at any time.

Answer 2

Answer: D)
`(7)/(15)`

Explanation:

Given : A wallet contains 4 dimes, 5 pennies, and 7 nickels.

Total coins = 4+5+7=16

Event A is defined as drawing a dime on the first draw and event B is defined as drawing a nickel on the second draw.

After 1st coin draws as dime , the total coins left = 16-1=15

Total nickels left as same as before.

Now,

Probability of drawing 2nd coin a nickel given that 1st one was a dime:

`P(B|A)=\frac{\text{Number of nickels}}{\text{Coins left}}\\\\=(7)/(15)`

Hence,
`P(B|A)=(7)/(15)`