Alan and his brother both want the last doughnut. alan makes a bet with his brother to decide who should get the doughnut. alan pulls out a standard deck of 5252 playing cards, shuffles it, and lets his brother pick a card without looking. alan decides he has the best chance to win if the bet is choosing a black card. his brother says there's a better chance of getting a card with a value of 1010 (given that an ace has a value of 11 and face cards have a value of 1010).

Bet should be placed on Black Cards.

In the question,

We have total 52 cards with us in the deck.

There are two cases of placing the bets,

One, when the card picked is black.

Second, when the card picked is a face card and a value of 10.

So,

Number of Black cards in the deck = 26

Number of Face cards with the value of 10 are = 4 x 3 = 12

So,

The probability of selecting a black card is given by,

Also,

Probability of selecting a face card of value 10 is given by,

Therefore, we can see the probability of picking a black card is more than the probability of selecting a face card of value 10.

Therefore, if the bet is placed on black card then there is the best chance to win.

it has to have an angle of 90 degrees