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    Question

    A box contains 6 red, 4 blue, 2 green and 4 yellow pencils.

    If four pencils are picked at random, what is the probability that at least two are of same colour?

    A 303/439 Correct Answer Incorrect Answer
    B 521/442 Correct Answer Incorrect Answer
    C 407/455 Correct Answer Incorrect Answer
    D 413/523 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    Total number of pencils = 6 + 4 + 2 +4 = 16 Let S be the sample space. Then, n(S) = total number of ways of drawing 4 pencils out of 16 = 16C4[if gte msEquation 12]>¹⁶ C 4 [if !msEquation]--> [endif]-->= `(16xx15xx14xx13)/(4xx3xx2xx1)` [if gte msEquation 12]>   16 × 15 × 14  × 13 4 × 3 × 2 × 1 [if !msEquation]--> [endif]-->= 1820 Let E= event of drawing 4 pencils when none is of same colour. n(E) = 6C1 X 4C 1 X 2C1 X 4C1 =`6xx4xx2xx4 = 192` [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->P (E) when none is of same colour =`192/1820` [if gte msEquation 12]> 192 1820 [if !msEquation]--> [endif]--> [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->P (E) when at least two are of same colour= 1 - `192/1820 = 1628/1820 = 407/455` [if gte msEquation 12]> 192 1820 [if !msEquation]--> [endif]-->

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