Question

All jacks, queens, and kings are removed from a pack of $52$ cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this cards is (i) a black face card (ii) a red card

Answer 1

Solution(i):

Given, All jacks, queens, and kings are removed from a pack of $52$ cards. There is no face card left to draw.

Hence, the probability of drawing a black face card is $0$.

Solution(ii):

As there are $6$ red face cards(king,queen,jack) and $6$ black face cards(king,queen,jack) in a pack $52$ cards , and those cards are removed so,

No. of cards in pack $=(52-12)=40$

No. of red cards $=20$ $i.e.,26-6$

Therefore, ${}^{20}{C}_1$( Selecting $1$ out of $20$ items) times out of ${}^{40}{C}_1$( Selecting $1$ out of $40$ items) a face card is picked.

Let $E$ be the event of getting a red card from the pack

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^{20}{C}_1}{{}^{40}{C}_1}$$=\frac{1}{2}$