Question

A boutique winery created a small batch of Dandelion wine for a wedding. Among 48 bottles, 13
bottles had leaking corks that resulted in Dandelion vinegar. The bride's father selected 6 bottles at
random to check the quality of wine. What is the probability that all 6 bottles are wine?
a-- 0.8497
b-- 0.8677
c--0.1323
d-- 0.1503
e-- 0.9998​

Answer 1

Given  :  A boutique winery created a small batch of Dandelion wine for a wedding. Among 48 bottles, 13 bottles had leaking corks that resulted in Dandelion vinegar. The bride's father selected 6 bottles at

random to check the quality of wine.

To Find  : the probability that all 6 bottles are wine  

a-- 0.8497

b-- 0.8677

c--0.1323

d-- 0.1503

e-- 0.9998​

Solution:

Total Bottles = 48

Vinegar = 13

Wine bottles = 48 - 13 = 35

6 bottles out of  48 can be selected in ⁴⁸C₆  ways

6 bottles of wines  can be selected in ³⁵C₆  ways

Probability  that all 6 bottles are wine  =  ³⁵C₆ / ⁴⁸C₆  

= 0.13227

= 0.1323

option c is correct

Probability  that all 6 bottles are wine  =  0.1323

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