Xavier Aptitude Test 2013 Paper

Question : 76 of 121

Marks: +1, -0

Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one of the cards drawn is a king, and b denote the probability of not drawing a king. The ratio a/b is

≥ 0.25 and ≤ 0.5
≥ 0.5 and ≤ 0.75
≥ 0.75 and ≤ 1.0
≥ 1.0 and ≤1.25
≥ 1.25

Validate

Solution:

(e) a = Probability of drawing at least 1 king out of 2 cards.

\ {P}(\ {a}) =\ {^{2} \ {C}_{1} \×^{4} \ {C}_{1}}{^{6} \ {C}_{2}}+\ {^{2} \ {C}_{2}}/{^{6} \ {C}_{2}} \

\ {2 \× 4 \× 2}/{6 \× 5}+ {2 ×1}/{6 \× 5}

=\ {8}/{15}+\ {1}/{15}= {9}/{15}

b = Probability of not drawing a king

\ {P}(\ {b})=\ {^{4} {C}_{2}}/{^{6} \ {C}_{2}}=\ {4 × 3}/{6 \× 5}=\ {6}/{15}

\∴ {\ {a}}/{\ {b}}=\ {9}/{6}=1.5

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