Bunuel wrote:
Official Solution:
A flower shop has 2 tulips, 2 roses, 2 daisies, and 2 lilies. If two flowers are sold at random, what is the probability of not picking exactly two tulips?
A. \(\frac{1}{8}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{2}\)
D. \(\frac{7}{8}\)
E. \(\frac{27}{28}\)
The probability of not picking exactly two tulips is 1 minus the probability of picking 2 tulips. Out of 8 flowers, there is a 2 out of 8 chance of picking a tulip: \(\frac{2}{8} = \frac{1}{4}\). Out of the 7 remaining flowers, there is a 1 out of 7 or \(\frac{1}{7}\) chance of picking a tulip. Multiply the two fractions together to get the probability of picking both tulips:
\(\frac{1}{4}*\frac{1}{7} = \frac{1}{28}\)
Find probability of not picking exactly two tulips using the following equation:
P (both not Tulips) = 1 - P(both Tulips)
\(1-\frac{1}{28} = \frac{28}{28}-\frac{1}{28} = \frac{27}{28}\)
Answer: E
one short cut way to solve is how it is done on right hand side
P(no tulip, no tuilp)+ P(tulip, no tulip)+P(no tulip, tulip) = 1- P( tulip,tulip) = 1- [( 2/8) X (1/7)]=27/28
lengthy and time consuming way is to solve right hand side method =P(no tulip, no tuilp)+ P(tulip, no tulip)+P(no tulip, tulip)
= [(6/8)X (5/7) + (2/8)X(6/7) + (6/8) X (2/7)] =27/28