SOLUTION: A basket contains two apples, three lemons, and one orange. If two fruits are drawn at random with replacement, find the probability of drawing: a) two apples b) one lemon on t

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Question 1184732: A basket contains two apples, three lemons, and one orange. If two fruits are drawn at random with
replacement, find the probability of drawing:
a) two apples
b) one lemon on the first draw and one orange on the second draw
c) one apple and one orange
d) one lemon on the first draw onlY

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
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A basket contains two apples, three lemons, and one orange. If two fruits are drawn at random with
replacement, find the probability of drawing:
a) two apples
b) one lemon on the first draw and one orange on the second draw
c) one apple and one orange
d) one lemon on the first draw only
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The notice common for parts  (a),  (b)  and  (c)  is that the total number of fruits is  2 + 3 + 1 = 6.


(a)  P = %282%2F6%29%2A%281%2F5%29 = %281%2F3%29%2A%281%2F5%29 = 1%2F15.    ANSWER


     The first  factor 2%2F6  is the probability to draw one of the two apples from the total of 6 fruits.

     The second factor 1%2F5  is the probability to draw the remaining single apple from the remaining 5 fruits.




(b)  P = %281%2F6%29%2A%281%2F5%29 = 1%2F30.    ANSWER


     The first  factor 1%2F6  is the probability to draw one lemon from the total 6 fruits.

     The second factor 1%2F5  is the probability to draw one orange from the remaining 5 fruits.




(c)  When we consider case (c), we should treat two cases P(apple,orange) + P(orange,apple).


     It may be boring.  There is another way  using combinations


          P = %28C%5B2%5D%5E1%2AC%5B1%5D%5E1%29%2FC%5B6%5D%5E2 = %282%2A1%29%2F15 = 2%2F15.    ANSWER




(d)  In case (d), I do not understand clearly what the question is, so I will not answer it.

Solved.