Question

Conditional Probability: A five digit number is formed from the digits 1, 2, 3, 4, and 5. What is the probability that the number ends in the digits 52, given that it is even?

Answer 1

is it that it ends in the digits 5 and 2, or that it ends in either 5 or 2?

Answer 2

i think 5 and 2 but them the second part says given that it is even but if it is 5 and 2 wouldn't it always be even?

Answer 3

if it means 5 or 2, then:

we have two events,
Event B is that is even and has probability of 2/5
Event A is that it ends in 5 or 2, and has a probability of 2/5.

We need Event A given Event B.
Formula is :
probability of a interesecting b over probability b

Answer 4

ok

Answer 5

intersection of a and b has a probability of 1/5

Answer 6

i will just use that

Answer 7

oh ok

Answer 8

because of the five numbers, only one of them is in both events.

Answer 9

the five right?, or no?

Answer 10

well the number 5 right? because its in both

Answer 11

one event is that it is 5 or 2, another is that it is even.
5 is not even!

Answer 12

ohh wow, my bad ok

Answer 13

so probability of a interesecting b over probability b will be:

(1/5) / (2/5)
= .2/.4
= 1/2 or 0.5

Answer 14

ok thank you, i think i get it now

Answer 15

would you help me on another problem or are you busy?

Answer 16

i can try

Answer 17

okay so the instructions say. A card is chosen from a standard deck of cards. Find the probability that the card is black. The question says: P(4)

Answer 18

how many cards are in a deck? and what is p4?

Answer 19

52 and i think card #4 in a deck

Answer 20

becuase other questions say P(facecard) or P(jack or ten)

Answer 21

does it use the word given in the question (e.g. black given that it is a 4) or just ask for the probability of a black 4?

Answer 22

oh yes it does i wrote it wrong: A card is chosen from a standard deck of cards. Find the probability Given that the card is black

Answer 23

ok, that is very important in probability questions. always look for it.

Answer 24

alright

Answer 25

how many options in a deck, sorry :)

Answer 26

1-10, + jack, queen and king? = 1/13?

Answer 27

whoops:
the probability of being black is 1/2,
the probability of being a 4 is 1/13

Answer 28

There are 52 cards in a standard deck of cards.
There are 26 black cards and 26 red cards in a deck.
There are 4 suits (Spades (black), Hearts (red), Diamonds (red), Clubs (black)), each consists of 13 cards, and they are Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2 in a deck.
There are 4 for every each type of cards (Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2) in a deck.
There are usually 2 Jokers in a deck.

Answer 29

so probability of a 4 in a suit is 1/13?

Answer 30

now, we need probability of 4 given black.
Our formula is
probability of a interesecting b over probability b

Answer 31

probability b is 1/2

Answer 32

yea i believe so

Answer 33

ok, and probability a intersecting b is the probability of getting a black and a four out of 52.
which is 2/52
because there are are 4 number fours, and two are red.

Answer 34

so probability of a interesecting b over probability b
is (2/52)/(1/2)

Answer 35

which gives me 1/13 ok thank you, would you mind helping me on another??, sorry

Answer 36

ill watch u do it.

Answer 37

ok i will try that out

Answer 38

With the same intrustions I have of :A card is chosen from a standard deck of cards. Find the probability Given that the card is black. And the question says P(6 of clubs)

Answer 39

so i know that i need 6 clubs out of the deck

Answer 40

what are the two events?

Answer 41

i think event B is 6/52 and event A is 4/52?

Answer 42

6 because of the 6 clubs

Answer 43

name the events.
event a is that ... will occur.
event b is that ... will occur.
then get the probabilities.

Answer 44

ok let me try so Event A is that 6 clubs out of 52 cards will occur?

Answer 45

no, its that you will get the six of clubs.

Answer 46

Event B is that 26 black cards out of 52 cards will occur?

Answer 47

event a is that when you pick a card you will get the six of clubs.
event b is that when you pick a card it will be black.

Answer 48

oh and a club has 13 cards

Answer 49

now what is the probability of event a, and what is the probability of event b?

Answer 50

how do you know which event is A or B?

Answer 51

good question. that is arbitrary, you can decide which is which, as long as you stick with it.

Answer 52

the probability of event A is 1/52. Since it is a 6 of clubs that is just one card right?

Answer 53

oh ok, i didnt know that

Answer 54

yep!

Answer 55

(just lookout for when the question has already told you which is a and which is b)

Answer 56

ok, the probability of b is?

Answer 57

ok and event B is that 2/52, since yea two of the 4's are red

Answer 58

try again. what are the chances of pickng a black card out of a deck?

Answer 59

event a is that when you pick a card you will get the six of clubs.
event b is that when you pick a card it will be black.

Answer 60

26 black cards in the deck. so 26/52

Answer 61

yep or 1/2

Answer 62

alright

Answer 63

now what is a intersecting b -
in other words, how many cards meet both criteria

Answer 64

divide both of the fractions right? event A over B

Answer 65

how man cards are both black and the six of clubs out of the fifty two cards?

Answer 66

1

Answer 67

bingo.

Answer 68

1/52?

Answer 69

now do we need a given b or b given a?

Answer 70

1/52 is correct

Answer 71

Find the probability Given that the card is black was the question.

event a is that when you pick a card you will get the six of clubs.
event b is that when you pick a card it will be black.

so we need a given b.

Answer 72

thank youuu! would you like to watch me do 3 more?? :), its my homework and this lesson confuses me but I think I am learning a lot right now

Answer 73

oh wait the problem isn't finished or did we finish it?

Answer 74

not yet

Answer 75

we have so far probability a, probability b, and we need probability a given b.

Answer 76

and we also have probability a intersecting b.

Answer 77

ohh ok, lets see how would i start to find that?

Answer 78

formula...

Answer 79

(always remember that probability of a intersecting b is different to a given b)

Answer 80

the formula would then be probability A intersecting B over B?

Answer 81

exactly. pr(a intersecting b) over pr(b)

Answer 82

okay

Answer 83

so what was pr(b)? (probability of picking a black card)?
and waht was pr (a intersecting b)? (probability of picking a card both black and 6 of clubs)?

Answer 84

is it 1/2 * 1/52 all over 1/2

Answer 85

its (1/52)/(1/2)

Answer 86

so the 1/2 cancels

Answer 87

oh ok ok

Answer 88

so 1/26 would be my answer?

Answer 89

showing that it is a 6 of clubs and that it is one of the black cards

Answer 90

yes.

Answer 91

yess ok

Answer 92

i have to go, but a small tip if i may,
to really understand probability and be good at it, its worth getting clear the difference between pr(a given b) and pr(a intersecting b), and understanding what they mean.
try and understand whats going on in each question, and not just use the formulas.

Answer 93

ok no problem thanks a million. I understood this more than being in my class. and you helped me for a while. I will review this chat for help if I am stuck. And ok I will try to do that. Thank Youu!

Answer 94

send me a message if u want help, and ill get back to you if i have time. (no promises)

Answer 95

good luck. probability takes a bit of time to get the hang of.

Answer 96

alrighty, thats fine

Answer 97

i want to understand it for the final so I will do the practice