Question

A standard deck consists of 52 cards,
1. One card is dealt. Find the chance that its color is black and its rank is an even number.
2.One card is dealt. Find the chance that its color is red or its rank is an even number.
3.A poker hand (5 cards) is dealt. Find the chance that the cards are all hearts.
4.A poker hand (5 cards) is dealt. Find the chance that the cards are all of the same suit. [This is sometimes called a “flush.”]

Answer 1

Chance is normally just a fraction
number of "good" outcomes / number of TOTAL outcomes...

Answer 2

i know that.. but there has to b some calculations as wel

Answer 3

There will be some number crunching... let's do number 1
How many black cards are there with even rank?

Answer 4

5

Answer 5

that is 2 4 6 8 10

Answer 6

Yeah... but there are two black suits, remember? :)

Answer 7

yes.. which makes a total of 10 even cards
ryt?

Answer 8

Correct. That makes 10 "good" outcomes... out of how many total?

Answer 9

52

Answer 10

so the answer will b?
10/52?

Answer 11

Yes. but reduce that to lowest terms...

Answer 12

5/26

Answer 13

now the second one

Answer 14

Second one... how many red cards are there?

Answer 15

26

Answer 16

so all 26 are good outcomes, right?

Answer 17

yeah

Answer 18

One card is dealt. Find the chance that its color is red or its rank is an even number.

Answer 19

but those aren't the only ones... we also consider all the even-ranked cards...
how many even ranked cards in all?

Answer 20

rather the card is red or its even

Answer 21

20 are even

Answer 22

20 are even, but 10 of them are red... how many of them aren't red?

Answer 23

10

Answer 24

so... 26 red cards plus 10 even-ranked cards (which aren't red) makes how many "good" outcomes?

Answer 25

36

Answer 26

it wll b 36/52?

Answer 27

yes. simplify please :)

Answer 28

9/13

Answer 29

good. :)

Answer 30

now 3 one

Answer 31

you're dealt one card, what's the chance that it's a heart?

Answer 32

1/13

Answer 33

nope :P

Answer 34

13/52?

Answer 35

good. simplify

Answer 36

that is not yet the answer, by the way.

Answer 37

then

Answer 38

still... might be easier if you simplify 13/52 first... go ahead now

Answer 39

1/4

Answer 40

okay... you've been given a heart for your first card... you're dealt a second card... what are the odds that it's a heart? :)

Answer 41

12/51

Answer 42

nice :)
so you've been given two hearts... what are the odds that a third one is a heart?

Answer 43

11/50

Answer 44

the fourth would be...?

Answer 45

10/49

Answer 46

and the fifth? :)

Answer 47

n 5th will b 9/48

Answer 48

Very nicely done.
Now multiply those 5 values, and you have your probability :)

Answer 49

ok

now 4th one

Answer 50

fourth one is similar to the third one, except the first card can be anything... so replace 1/4 with 52/52
which is just 1 :)

Answer 51

ahan

the answer of 2rd one will b
33/66640

Answer 52

3rd?

Answer 53

that's the 3rd...

Answer 54

and 4th one
11/4165?

Answer 55

as long as you multiplied the answer to the 3rd by 4, you get the answer to the 4th :)

Answer 56

cant get this one

Answer 57

Okay, you pick a card, you know its suit, right?

Answer 58

umm

Answer 59

You pick a second card, what are the chances that it's the same suit?

Answer 60

12/51?

Answer 61

good... the third card? chances that it's the same suit?

Answer 62

11/50
and 4th one will b
10/49

Answer 63

and the fifth.

Answer 64

9/48

Answer 65

multiply them now.
It's just like in the 3rd, except no 1/4 in the beginning.

Answer 66

the answer will b
33/16660?

Answer 67

as long as you did the arithmetic properly (I have no calculator with me)

Answer 68

ahan
its ryt