Question 1199667: Jon buys a bag of cookies that contains 7 chocolate chip cookies, 6 peanut butter cookies, 8 sugar cookies and 5 oatmeal cookies. What is the probability that Jon randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a sugar cookie?
Probability =
(Round to 4 decimal places)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
A = event of selecting a chocolate chip cookie on the 1st selection
P(A) = (number of chocolate chip)/(number total)
P(A) = (7 chocolate chip)/(7+6+8+5 total)
P(A) = (7 chocolate chip)/(26 total)
P(A) = 7/26
The fact that Jon eats the 1st cookie means no replacement is done.
This will affect the probability of the 2nd cookie (hence the events aren't independent).
B = event of selecting a sugar cookie on the 2nd selection
P(B given A) = probability B happens if event A happened
P(B given A) = (number of sugar cookies)/(total number left)
P(B given A) = (8 sugar cookies)/(26-1 left over)
P(B given A) = (8 sugar cookies)/(25 left over)
P(B given A) = 8/25
For more information, search out "conditional probability".
Lastly,
P(A and B) = P(A) * P(B given A)
P(A and B) = (7/26)*(8/25)
P(A and B) = 0.08615384615384 approximately
P(A and B) = 0.0862
There's about an 8.62% chance of this happening.
-----------------------------------------------------
Answer: 0.0862
|
|
|
