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    Subject

    Quantitative Aptitude

    Topic

    Probability

    Two cards are drawn at random from a well - shuffled pack of 52 cards. what is the probability that either both are red or both are queens?

    ক)
    17/112
    খ)
    55/221
    গ)
    55/121
    ঘ)
    33/221

    Explanation

    n(S) = 52C2{}^{52}C_2 = 1326 Let  A = event of getting both red cards and B = event of getting both queens then (A∩B)\left(A\cap B\right) = event of getting two red queens n(A) = 26C2{}^{26}C_2 = 325,   n(B) = 4C2{}^4C_2 = 6 n(A∩B)=2C2=1n(A\cap B)={}^2C_2=1 ∴  P(A)=3251326,  P(B)  =  61326\therefore\;P\left(A\right)=\frac{325}{1326},\;P\left(B\right)\;=\;\frac6{1326} P(A∩B)=11326P\left(A\cap B\right)=\frac1{1326} P ( both red or both queens) = P(A∪B)P\left(A\cup B\right) = P(A)+P(B)−P(A∩B)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)= 3251326+1221−11326\frac{325}{1326}+\frac1{221}-\frac1{1326} = 55221\frac{55}{221}

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