Probability MCQ 4( two cards are drawn one after the other)
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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