Four cards will be dealt off the top of a well-shuffled deck. There are two options. (i) To win $10 if the first card is club and the second is a diamond and the third is a heart and the fourth is a spade. (ii) To win $10 if the four cards are of four different suits. Compute the probability of winning $10 for each case. Which option is better

0.0043957 ; 0.105498 ; 2nd option is better

Step-by-step explanation:

Option 1:

First card :P(club) = 13/52

Second card: P(diamond) = 13/51

Third card : P(heart) = 13 / 50

Fourth card: P(spade) = 13/49

Hence,

P(club, diamond, heart, spade) = (13/52) * (13/51) * (13/50) * (13/49) = 0.0043957

Probability of winning $10 = 0.0043957

2nd option:

P(card of different suit) [order of arrangement does not matter]

(13C1 * 13C1 * 13C1 * 13C1) / 52C4

= 28561 / 270725

= 0.105498

Probability of winning $10 = 0.105498

Because the probability of winning for the second option is higher than for the first option, then the second option is better.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

2160ft3

step-by-step explanation: