Question

From a box of fruit containing 37 oranges and 1 apple a random sample of 2 pieces of fruit has been selected without replacement. Let X be the number of oranges and Y be the number of apples in the sample. What will the expected value of X, E(X)?

Answer 1

'X' is the number of oranges. Since we are selecting two fruits without replacement out of total of 38 fruits (37 O + 1A)

we can do it in = 38C2 ............using combination function

= 703 ways ..................nCr =

  Now for choosing oranges.

Either we can have both oranges or we can have 1 orsnge. We can't have 0 oranges since there is only 1 apple so we are sure that there will be atleast 1 orange.

No. of ways of getting 2 orange out of 37 = 37C2

= 666

P(2 oranges) = 666 / 703 = 0.9474 ..........we divide our likely to our total outcomes to get the probability

No. of ways of getting 1 orange and therefore 1 apple = 37C1 * 1C1 ........first for orange and 2nd for appple

=37

P(1 orange) = 37 / 703 = 0.0526

No of oranges (X)	P(X)	X * P(X)
1	0.0526	0.0526
2	0.9474	1.8947
Total	1	1.9474