Question

How can we increase the probability of getting `2` face cards i a row to the highest level? (a) removing all black cards or (b) removing all non-face cards.

Answer 1

It is quite apparent that removing all non-face cards will leave only face cards in the deck and as there is no chance of getting non-face cards, the probability of getting `2` face cards in a row will be `1`, the highest.

Answer 2

The second option is the desired answer because it is the only one that increases the chances.

Explanation:

Let's look at each action:

Removing all the black cards.
There will be only red cards left, but the fraction of face cards still remains the same. This action therefore has no effect on drawing the first face card, but slightly decreases the chance of getting a second..

All red:
`P(F,F) = 6/26 xx 5/25 = 30/650 = 0.0462 = 46.2%`

Whole deck:
`P(F,F) = 12/52 xx 11/51 = 132/2652=0.0498 = 49.8%`

Removing all the non-face cards
All cards are either face-cards or non-face cards, so if you remove all the non-face cards from the deck, there are only face cards left. Rather than just increasing the chance of getting a face-card, this action guarantees the result . `(F,F) = 12/12 xx11/11 = 1`

Removing all the kings
If the 4 kings are taken out of the deck there will be fewer face-cards left. (8 instead of 12). This action decreases the chance of getting a face-card.
`P(F,F) = 8/52 xx 7/51 =56/2652 = 0.0211 = 21.1%`

Removing all the red cards
The effect is the same as removing all the black cards.