Shue a full deck of cards and turn them over one by one until an Ace appears. It turns out that this happened exactly when the 20th card was turned over. What is the probability that the next card is (a) the ace of spades; (b) the two of clubs

Step-by-step explanation:

In a standard deck of cards, there 54 cards (52 cards plus 2 Jokers). There are 4 suits (kinds of shapes) in a deck namely: Clubs, Diamonds, Hearts and Spades. Each of the suits numbers from number 2 to number 10 (numbering 36 cards). Afterwards, we have 4 suits each for the Jack, Queen, King & Ace cards (numbering 16 cards). And then 2 Jokers

An Ace turned up at the 20th card, this means there 34 cards left. The number of cards left is given by the difference between 54 & 20. Mathematically shown below:

Cards left = 54 - 20 = 34

Total number of cards = 54, number of Aces of Spades ♠ in the deck = 1, number of two clubs ♣ in the deck = 1

A. Probability of the next card being Ace of Spades ♠ = the number of Ace of Spades card in the deck ÷ Total number of cards left in the deck

Pr (Ace of Spades) = 1 ÷ 34

Pr (Ace of Spades) = 0.0294 or 2.94%

B. Probability of the next card being Two of Clubs ♣ = the number of Two of Clubs card in the deck ÷ Total number of cards left in the deck

Pr (Two of Clubs) = 1 ÷ 34

Pr (Two of Clubs) = 0.0294 or 2.94%

It therefore implies that the chancess of the next card being Ace of Spades (A ♠) or Two of Clubs (2 ♣) is the same; the Ace of Spades is just equally as likely to be picked as the next card from the deck as Two of Clubs

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺