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Nilima Omar Sastry
Asked: 2022-11-04T01:09:24+05:30 In:

A box I contain letters of 3 white, 1 blue and 2 yellow color another box II contain letters of 5 white, 3 blue and 4 yellow color, if all the letters are mixed in box III and 2 letters are picked without replacing, then what is the possibility that the letters are not white?
1. \(7\over 17\)
2. \(4\over 9\)
3. \(10\over 17\)
4. \(5\over 17\)

A box I contain letters of 3 white, 1 blue and 2 yellow color another box II contain letters of 5 white, 3 blue and 4 yellow color, if all the letters are mixed in box III and 2 letters are picked without replacing, then what is the possibility that the letters are not white?
1. \(7\over 17\)
2. \(4\over 9\)
3. \(10\over 17\)
4. \(5\over 17\)
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  1. Correct Answer – Option 4 : \(5\over 17\)

    Concept: 

    General Rule:

    • The number of ways for selecting r from a group of n (n > r) = nCr 
    • The probability of particular case = \(\rm \text{Number of ways for the case can be executed}\over{\text{Total number of ways for selection}}\)

     

    Calculation:

    The total letters in box III = 3 + 1 + 2 + 5 + 3 + 4 = 18

    Out of which:

    White letters = 3 + 5 = 8

    Blue letters = 1 + 3 = 4

    Yellow letters = 2 + 4 = 6

    Ways of selecting 2 letters out of 18 without replacement = 18C2

    Ways of selecting 2 letters out of 10 not white letters without replacement = 10C2  

    Possibility of the letters picked are not white = \(\rm ^{10}C_2\over^{18}C_2\) = \(5\over 17\)

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