Determine whether the event is independent or dependent. Then find the probability.

There are 6 green, 2 red, 2 brown, 4 navy, and 2 purple marbles in a hat. Sadie picks 2 marbles from the hat without replacement. What is the probability that the first marble is brown and the second marble is not purple?

Respuesta :

Answer:

Dependent

18.46%

Step-by-step explanation:

All possible combinations for Sadie taking two marbles out from the hat:

[tex](6+2+2+4+2)×[(6+2+2+4+2)-1] [/tex]

[tex] = 16 \times 15[/tex]

[tex] = 240[/tex]

All the possible combinations that the first marble is brown and the second marble is not purple:

[tex]2 \times (6 + 2 + 1 + 4)[/tex]

[tex] = 2 \times 13[/tex]

[tex] = 26[/tex]

The probability:

[tex] \frac{240}{26} \times 100\%[/tex]

[tex] = \frac{240}{13} \times 50\%[/tex]

[tex] = \frac{1200}{13} \%[/tex]

[tex]≈18.46%[/tex]