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Question

A box contains 10 green, 20 red, 30 Black and 40 orange marbles. One marble is drawn from the box at random. The probability that marble is neither green nor orange is

A
12
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B
710
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C
35
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D
None of these
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Solution

The correct option is A 12
Let's denote green colored marbles with G, red colored with R,black colored with B and orange with O.
given P(G)=10100=0.1,

Similarly,P(R)=0.2,P(B)=0.3,P(O)=0.4
Let the desired event be denoted by E.
P(GcOc)=1P(GO)=1P(G)P(O)+P(G)P(O)P(GcOc)=P(E)=10.10.4+0

P(G)P(O)=0 because one marble can't be of two different colors.
P(GcOc)=P(E)=10.10.4+0=12

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