1. Marciano draws five cards from a 52-card deck. Calculate the probability of each given event. a. Two cards are sevens, given there are no face cards b. There is exactly one face card, given three of the cards are red c. Three cards are Aces, given one of the Aces was removed from the deck

Step-by-step explanation:

In a standard deck of 52 cards, face cards are cards with faces on them. There are 12 of them, 3 in each suit. They are also called “court cards,” because they show Kings, Queens and Jacks.” An Ace cannot be considered a “face card,” for the simple reason that it has no face on it.

a) Two cards are sevens, given there are no face cards

 = ( 52- 12 face cards = 40)

 =  ( 4÷40×3÷40 = 0.1×0.075 = 0.0075 ( or) 0.75%

b. There is exactly one face card, given three of the cards are red

Total cards=  (52-11 =41 cards)

assumed that the exactly one face card is not a red card

Red cards = (26-6 red face cards = 20 cards )

Picking Three red cards

=(20÷41 ×19÷40×18÷39 =0.487 ×0.475 ×0.461 =0.107 or 11%

c. Three cards are Aces, given one of the Aces was removed from the deck

Total cards = (52-1 ace card = 51 cards)

Picking three cards are ace

= (3÷51 ×2÷50×1÷49 = 0.059×0.04×0.02 = 0.0000472

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.