Answer to Question #142128 in Statistics and Probability for qwerty

Question

4. Find the probability of randomly selecting 4 good quarts of milk in succession from a cooler containing 25 quarts of which 5 have spoiled, by using:

(a) Theorem 3 of the product rule
(b) the concept of probability of events

Answer 1

There are 25 quarts of which 5 are spoiled. Hence there are 20 good quarts.

a) product rule:

P(4 good quarts) = P(1st is good AND 2nd is good AND 3rd is good AND 4th is good) =

= P(1st is good) * P(2nd is good) * P(3rd is good) * P(4th is good) =

= $\frac{20}{25}\cdot\frac{19}{24}\cdot\frac{18}{23}\cdot\frac{17}{22}=0.38$

b) the concept of probability of events:

Number of selecting 4 good quarts is combination:

$C(20,4)=\frac{20!}{4!16!}=4845$

Number all possible outcomes selecting 4 quarts:

$C(25,4) =\frac{25!}{4!21!}=12650$

P(4 good quarts) = $\frac{C(20,4)}{C(25,4)}=\frac{4845}{12650}= 0.38$