suppose that you have 4 green cards and 5 yellow cards. the cards are well shuffled. you randomly draw two…

suppose that you have 4 green cards and 5 yellow cards. the cards are well shuffled. you randomly draw two cards without replacement. round answers to 4 decimal places.\ng1 = the first card drawn is green\ng2 = the second card drawn is green\na. p(g1 and g2) =\n\nb. p(at least 1 green) =\n\nc. p(g2|g1) =\n\nd. are g1 and g2 independent?\n\nthey are independent events\nthey are dependent events\nhint: independent events \nvideo on independent events +

suppose that you have 4 green cards and 5 yellow cards. the cards are well shuffled. you randomly draw two cards without replacement. round answers to 4 decimal places.\ng1 = the first card drawn is green\ng2 = the second card drawn is green\na. p(g1 and g2) =\n\nb. p(at least 1 green) =\n\nc. p(g2|g1) =\n\nd. are g1 and g2 independent?\n\nthey are independent events\nthey are dependent events\nhint: independent events \nvideo on independent events +

Answer

Explanation:

Step1: Calculate total number of cards

Total cards = 4 (green) + 5 (yellow)=9 cards.

Step2: Calculate P(G1 and G2)

P(G1)=$\frac{4}{9}$, after drawing a green - card first, there are 3 green cards left and 8 total cards left. So P(G2|G1)=$\frac{3}{8}$. By the multiplication rule P(G1 and G2)=P(G1)×P(G2|G1)=$\frac{4}{9}\times\frac{3}{8}=\frac{12}{72}\approx0.1667$.

Step3: Calculate P(At least 1 green)

P(At least 1 green)=1 - P(no green). P(no green) means drawing two yellow cards. P(first yellow)=$\frac{5}{9}$, P(second yellow|first yellow)=$\frac{4}{8}$. So P(no green)=$\frac{5}{9}\times\frac{4}{8}=\frac{20}{72}$. Then P(At least 1 green)=1 - $\frac{20}{72}=\frac{52}{72}\approx0.7222$.

Step4: Calculate P(G2|G1)

As calculated in Step 2, if the first card is green, there are 3 green cards and 8 total cards left. So P(G2|G1)=$\frac{3}{8}=0.3750$.

Step5: Determine independence

Two events G1 and G2 are independent if P(G2|G1)=P(G2). P(G2)=$\frac{4}{9}$ (before any card is drawn), and P(G2|G1)=$\frac{3}{8}$. Since P(G2|G1)≠P(G2), G1 and G2 are dependent events.

Answer:

a. 0.1667 b. 0.7222 c. 0.3750 d. They are dependent events