Question

Five cards are drawn from a deck of cards; Each card is replaced after being drawn. What is the probability of the following event: P(3 and 3 and 3 and 2 and 2)?

Answer 1

can u just find the probability P(3) and P(2) ?

Answer 2

I think that's what it's asking

Answer 3

ok, how many cards are there in the deck ?

Answer 4

I have no clue :/

Answer 5

ohh.... there are total, 52 cards in a deck.
13 of clubs
13 of hearts
13 of spades
13 of diamonds

Answer 6

Okay

Answer 7

now u are drawing 5 cards from 52 cards.
when u draw one card , the probability of card being 2 is 4/52
because there are 4 '2' in the deck.
got this ?

Answer 8

Yes.

Answer 9

similarly the probability of drawing a '3' is 4/52=1/13.
so u have P(2)=1/13 and P(3) = 1/13
ok with this ?

Answer 10

Yes.

Answer 11

since the events of drawing 2 and drawing 3 are independent.
we have:P(3 and 3 and 3 and 2 and 2) = P(3)P(3)P(3)P(2)P(2)
ok with this next step ?

Answer 12

Yes.

Answer 13

so :P(3 and 3 and 3 and 2 and 2) = (1/13)*(1/13)*(1/13)*(1/13)*(1/13)=(1/13)^5
got this ?

Answer 14

Okay, Yes.

Answer 15

thats your final answer:
(1/13)^5 or 1/(13)^5 or 1/(371293)

Answer 16

Thank you! :) I don't get how you got 1/13 though?

Answer 17

u got how i wrote 4/52 ?

Answer 18

Yes, because there's 4 '2' in a deck. What does that mean though? 4 what in a deck?

Answer 19

every deck contains 52 cards. 4 suits, which i mentioned. each suit has 13 cards from A,2,3,4,5,6,7,8,9,10,J,Q,K
hence there will be 4 '2's of each suit.

Answer 20

*there will be 4 '2's, one of each suit.

Answer 21

hence the probability of selecting a '2' is 4/52 = 1/13

Answer 22

Alright I got it now. Thank you :)

Answer 23

welcome :)

Answer 24

I might post another one that i'm a little condfused on, Can you help me?

Answer 25

sure :)