Question

4.96

In one area of an orchard, there are 17 trees, of which 10 are bushy and 7 lean. If 4 trees are randomly selected for testing a new spray, what is the probability that exactly 2 bushy trees are selected? 

4.97 

Referring to Exercise 4.96, now suppose that the trees are located in two rows: Row A has 8 trees of which 4 are bushy, and row B has 9 trees of which 6 are bushy. Two trees are to be randomly selected from each row for testing the spray, and the selections are independent for the two rows. 

(a) Find the probability that the trees selected in row A are both bushy and those selected in row B are both lean.

(b) Find the probability that of the total of4 trees selected in the manner described above, exactly 2 are bushy.

Answer 1

4.96) from Hypergeometric distribution:

P(exactly 2 are bushy) =P(selecting 2 from 10 bushy and 2 from 7 lean) = =0.3971

4.97)

a)P(both from A are bushy and both lean from B) ==0.2143*0.0833 =0.0179

b)P(2 are bushy)=P(from A 2 bushy and from B 0+from A 1 bushy and from B 1+from A 0 bushy and from B 2)

=

=0.2143*0.0833+.5714*0.5+.2143*.4167 =0.3929

( please revert for any clarification)