Question

use this for questions 5 and 6 below: a basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. mark chooses a piece, eats it, then selects another (without replacement).

1. p(green then nectarine)

a. 2363 b. 5162 c. 1336 d. 263

Explanation:

Step1: Calculate total number of fruits initially

Total fruits = \(8 + 11+5 + 12=36\)

Step2: Calculate probability of first picking a green apple

Number of green apples \(n(G)=8\). Probability \(P(G)=\frac{8}{36}\)

Step3: Calculate probability of then picking a nectarine (after one fruit is eaten)

After eating one fruit (a green apple), total fruits left \(=36 - 1=35\). Number of nectarines \(n(N)=5\). Probability \(P(N|G)=\frac{5}{35}\)

Step4: Calculate the joint probability (using multiplication rule for dependent events \(P(A\cap B)=P(A)\times P(B|A)\))

\(P(\text{green then nectarine})=\frac{8}{36}\times\frac{5}{35}=\frac{40}{1260}=\frac{2}{63}\approx0.0317\)

Answer:

D. \(2/63\)