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

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BasketballEinstein BasketballEinstein · Answer 1 · 2019-10-05T19:28:36+02:00

Answer:

A.) ¼

Step-by-step 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

[tex]\frac{1}{4} = \frac{4}{16}[/tex]

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

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JeanaShupp JeanaShupp · Answer 2 · 2019-10-15T09:19:38+02:00

Answer: D) [tex]\dfrac{7}{15}[/tex]

Step-by-step 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:

[tex]P(B|A)=\dfrac{\text{Number of nickels}}{\text{Coins left}}\\\\=\dfrac{7}{15}[/tex]

Hence, [tex]P(B|A)=\dfrac{7}{15}[/tex]