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(\text{green then nectarine}) )

a. 2/63 b. 5/162 c. 1/336 d. 2/63

1. ( p(\text{two oranges}) )

a. 1/9 b. 4/35 c. 11/105 d. 68/105

Explanation:

Step1: Calculate total number of fruits

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

Step2: Calculate \(P(\text{green})\)

\(P(\text{green})=\frac{8}{36}\)

Step3: Calculate \(P(\text{nectarine}|\text{green})\)

After eating a green apple, total fruits \(=35\), \(P(\text{nectarine}|\text{green})=\frac{5}{35}\)

Step4: Calculate \(P(\text{green then nectarine})\)

By multiplication rule \(P(A\cap B)=P(A)\times P(B|A)\), \(P(\text{green then nectarine})=\frac{8}{36}\times\frac{5}{35}=\frac{40}{1260}=\frac{2}{63}\)

Step5: Calculate \(P(\text{two oranges})\)

\(P(\text{first orange})=\frac{12}{36}\)
After eating an orange, total fruits \(=35\), \(P(\text{second orange}|\text{first orange})=\frac{11}{35}\)
By multiplication rule \(P(\text{two oranges})=\frac{12}{36}\times\frac{11}{35}=\frac{132}{1260}=\frac{11}{105}\)

Answer:

1. D. \( \frac{2}{63}\)
2. C. \( \frac{11}{105}\)