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Probability MCQ2: (Shuffled Cards)

Probability MCQ2: What is probability of drawing two clubs from a well shuffled pack of 52 cards?

a) 13/51              b) 1/17            c) 1/26           d) 13/17

Solution:

Let the first club card draw event=A

and

Let probability of first card being the club card = P(A)

Similarly,

Let second club card draw event =B

and

Let the probability of second card being the club card=P(B)

When we draw first time – there are are 13 club cards (keep in mind for playing cards! )

So probability of first club card is:

\[ P(A)=\frac{13}{52}=\frac{1}{4} \]

After first draw, there will be left 51 cards as total sample and number of club cards will be 12 so,

the probability of second club card is:

\[ P(B)=\frac{12}{51} \]

Since events are independent of each other, in statistics we have the rule;

P(A and B)=P(A) . P(B)    (dot shows multiplication)

So,

Probability of first and second time a club cards is;

\[ P(A andB)=P(A)\times P(B)=\frac{1}{4}\times\frac{12}{51}=\frac{1}{17} \]

so the option ‘b’ is correct!

 

 

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