Question

all the three face cards of club are removed from the pack of 52 cards a card is drawn at random from the remaining pack find the probability of getting red card and King card ​

Answer 1

So the three face cards, i.e., king, queen and jack, of clubs are removed from the deck of 52 cards. Now we have only 52 - 3 = 49 cards.

So the probability of taking one card from the 49 ones is $^{49}\!C_1=49.$

Thus, $n(S)=49$ where S is the sample space.

Well, the hearts cards and diamond cards are the red cards. So the event that of getting a red card should be,

$R=\{x:x\in H\ \lor\ x\in D\}\\\\R=H\cup D$

where H is the set of hearts cards and D is that of diamond cards.

The event that of getting a king card is,

$K=\{K_D,\ K_H,\ K_S\}$

where d, h and s correspond to diamond, heart and spade respectively. Since king of clubs is removed, $K_C$ won't include.

Now, the event of getting a red card 'and' a king card is,

$E=R\cap K\\\\E=\{K_D,\ K_H\}$

Thus,

$n(E)=2$

Hence, probability is,

$P(E)=\dfrac {n(E)}{n(S)}\\\\\\\boxed {P(E)=\mathbf{\dfrac {2}{49}}}$

#answerwithquality

#BAL