Question

A gardener has fourteen identical looking tulip bulbs, of which seven will produce

Answer 1

Answer:$94.872\ \%$

Step-by-step explanation:

Given

There are 14 bulbs out of which 7 are Yellow and 7 are Pink

If a gardener randomly select 6 bulbs

Then the Probability that at least two of them are yellow

i.e. $=1-P(\text{0 Yellow})-P(\text{1 Yellow})$

Probability of choosing a 0 yellow (i.e. 6 pink bulbs )

$P(0)=\dfrac{^7C_0\times ^7C_6}{{14}^C_{6}}$

$P(1)=\dfrac{^7C_1\times ^7C_5}{{14}^C_{6}}$

Now the required Probability is

$P=1-\dfrac{^7C_0\times ^7C_6}{{14}^C_{6}}-\dfrac{^7C_1\times ^7C_5}{{14}^C_{6}}$

$P=1-[\dfrac{7+7\times 21}{3003}]$

$P=1-\frac{28}{3003}$

$P=0.9487$

i.e. $94.872\ \%$