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Probability MCQ 4( Cards drawn, replacement)

Probability MCQ 4: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is_

A. 1/26            b) 3/52                c) 15/26                 d) 11/26

Solution:

Before proceeding to solution – keep in mind that a pack of playing cards has 52 cards – in which there are 4 suits of 13 cards each.

Each suit has name – spade,  hearts, diamonds and clubs.

Each suit has its king – 4 kings there are in a pack!

Spades and diamonds are black color cards i-e there are  total 26 black cards!

Hearts and diamonds are red cards i-e 26 red cards!

For probability of an event ‘A’ we have formula;

\[ P(A) = \frac{ Number of favorable outcomes}{ Total number of possible outcome } \]

So if E1 is event of drawing a red card then;

\[ P(E1)=\frac{Red Cards}{Total Cards}=\frac{26}{52}=\frac{1}{2} \]

If E2 is event of drawing a king then;

\[ P(E2)=\frac{ Total Kings}{TotalCards}=\frac {4}{52}=\frac{1}{13} \]

Since there is replacement after first draw i-e after drawing the card it is put back into the pack and hence again no. of cards becomes 52, the probability of drawing a red card or a king card is equal or independent of each other !

Formula for independent probability of independent events E1 and E2 is;

\[ P(E1 \cap E2)=P(E1)\times P(E2) \]

\[ = \frac{1}{2}\times \frac{1}{13}=\frac{1}{26} \]

 

So the probability that first card is red and second is black — and vice versa – is 1/26

 

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