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There are 3 red, 6 blue, 5 yellow, and 4 green hair bands in a bag. Morgan wants a blue hair band and a yellow hair band to wear to school. What is the probability of picking a yellow hair band followed by a blue hair band, if the first hair band drawn is not replaced?

Respuesta :

To find the answer we need to use conditional probability:

[tex]P(B\cap A)=P(A)P(B|A)[/tex]

In this case event A is picking a yellow band and event B is picking a blue band second.

Then:

[tex]P(A)=\frac{5}{18}[/tex]

and:

[tex]P(B|A)=\frac{6}{17}[/tex]

Then the probability we are looking for is:

[tex]P(A\cap B)=\frac{5}{18}\cdot\frac{6}{17}=\frac{5}{51}[/tex]