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A gardener has fourteen identical looking tulip bulbs, of which seven will produce
yellow tulips and seven will become pink. She randomly selects and plants six of
them and then gives the rest away. When the flowers start to bloom, what is the
probability that at least two of them are yellow?
73.81%
94.872%
52.914%
89.977%

Respuesta :

Answer:[tex]94.872\ \%[/tex]

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. [tex]=1-P(\text{0 Yellow})-P(\text{1 Yellow})[/tex]

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

[tex]P(0)=\dfrac{^7C_0\times ^7C_6}{{14}^C_{6}}[/tex]

[tex]P(1)=\dfrac{^7C_1\times ^7C_5}{{14}^C_{6}}[/tex]

Now the required Probability is

[tex]P=1-\dfrac{^7C_0\times ^7C_6}{{14}^C_{6}}-\dfrac{^7C_1\times ^7C_5}{{14}^C_{6}}[/tex]

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

[tex]P=1-\frac{28}{3003}[/tex]

[tex]P=0.9487[/tex]

i.e. [tex]94.872\ \%[/tex]

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