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Suppose that you have 10 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places.G1 = the first card drawn is greenG2 = the second card drawn is greena. P(G1 and G2) =b. P(At least 1 green) =c. P(G2|G1) =d. Are G1 and G2 independent?

Respuesta :

Answer:

Yes

Step-by-step explanation:

Cricetus

The probability according to the given question will be:

  • (a) 0.4286
  • (b) 0.90477
  • (c) 0.64286
  • (d) No, they are dependent.

Given values are:

Number of green cards,

  • 10

Number of yellow cards,

  • 5

Total number of cards,

  • 15

(a)

→ [tex]P(G_1 \ and \ G_2) = (\frac{10}{15} )\times (\frac{9}{14} )[/tex]

                          [tex]= \frac{5}{5}\times \frac{3}{7}[/tex]

                          [tex]= 0.4286[/tex]

(b)

→ [tex]P(At \ least \ one \ green) = 1-P(No \ green)[/tex]

                                       [tex]= 1-(\frac{5}{15}\times \frac{4}{14} )[/tex]

                                       [tex]= 1-(\frac{1}{3}\times \frac{2}{7} )[/tex]

                                       [tex]= 0.90477[/tex]

(c)      

→ [tex]P(G_2 | G_1) = \frac{P(G_2 \ and \ G_1)}{P(G_1)}[/tex]

                   [tex]= \frac{0.4286}{(\frac{10}{15}) }[/tex]

                   [tex]= \frac{0.4286}{(\frac{2}{3} )}[/tex]

                   [tex]= 0.64286[/tex]

(d) [tex]G_1[/tex] and [tex]G_2[/tex] are dependent.

Thus the above response is correct.

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