The king, queen and jack of clubs are removed

Question:

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at fandom from the

remaining cards. Determine the probability that the card is

(i) a heart                                       

(ii) a king

Solution:

If we remove one king, one queen and one jack of clubs from 52 cards, then the remaining

cards left, n(S) = 49

(I) Let $E_{1}=$ Event of getting a heart

$n\left(E_{1}\right)=13$

$\therefore$ $P\left(E_{1}\right)=\frac{n\left(E_{1}\right)}{n(S)}=\frac{13}{49}$

(ii) Let $E_{2}=$ Event of getting a king

$n\left(E_{2}\right)=3 \quad$ [since, out of 4 king, one club cards is already removed]

$\therefore$ $P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{3}{49}$

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