Question

ok so,
a bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random one marbles drawn and replaced. then the second is drawn
1. what is the probability of selecting a purple marble and then a white marble?
2. what is the probability of selecting two white marbles?
3. is there a greater chance of selecting two white marbles in row or two purple marbles in row?

Answer 1

i really need help please i dont understand

Answer 2

let's break the problem down step by step:

1. how many purple marbles are there?
2. how many total marbles are there?

Answer 3

7

Answer 4

yes, there are 7 purple marbles.

how many total marbles are there?

Answer 5

9

Answer 6

Excellent! so what is the probability of getting a purple marble?

Answer 7

7/9?

Answer 8

yes!

since the problem says "with replacement" that means that after we put the purple marble back, there are still 7 purple marbles and 2 white marbles.

my next question: what is the probability of getting a white marble?

Answer 9

2/9

Answer 10

great, you're doing very well so far!

ok, so #1 is asking "what is the probability of getting a purple marble AND a white marble"

that means you have to multiply the probability of getting a purple marble, times the probability of getting a white marble

Answer 11

in other words, the probability of getting purple, then white is: (probability of getting purple)*(probability of getting white)

Answer 12

so 7/9 X 2/9?

Answer 13

yup!

Answer 14

ok one sec

Answer 15

0.17283950617

Answer 16

uh, you don't have to do that, you can just leave it as a fraction

(7/9)*(2/9) = 14/81, do you agree?

Answer 17

oh ok yes

Answer 18

ok, do you think you can answer #2?
2. what is the probability of selecting two white marbles?

Answer 19

ummmmm 7/81?

Answer 20

14/81 right

Answer 21

hint: probability of getting a white marble: 2/9

Answer 22

no, the answer to number 1 is 14/81, let's find the answer to number 2 using the same logic

probability of getting two white marbles = (probability of getting one white marble)*(probability of getting one white marble)

Answer 23

ok

Answer 24

that would be 1/9 right?

Answer 25

si 1/9 x 1/9

Answer 26

not quite, please remember step 1:

what is the probability of getting a white marble?
there are 2 white marbles and 9 total marbles, remember?

Answer 27

yes

Answer 28

the probability of getting one white marble is 2/9, do you agree?

Answer 29

yes

Answer 30

so 2/9 x 2/9???

Answer 31

YES! excellent! you just finished #2, let's work on #3

what is the probability of getting two purple marbles?

Answer 32

so two is 4/81 right

Answer 33

?????

Answer 34

yes, number 2 is 4/81

Answer 35

let's work on number 3:

what is the probability of getting two purple marbles?

Answer 36

7/9 x 7/9?

Answer 37

great! now, what is the probability of getting two white marbles?

Answer 38

49/81 and 4/81?

Answer 39

great! now, which number is bigger?

Answer 40

49/81

Answer 41

great, so, can you answer question #3 now?

Answer 42

is there a greater chance of selecting two white marbles in row or two purple marbles in row?

purple or white, which one is bigger?

Answer 43

yes there is a greater chance a of getting 2 purple marble than 2 white marbles

Answer 44

AWESOME! you're done ~

Answer 45

THANK YOU SO MUCH