Question

A jar contains 8 green, 5 red, 4 blue, and 3 black marbles.once a marble is selected, it is not replaced. find each probability.
1) p(two green marbles)
2) p(two black marbles)
3) p(a red marble and then a blue marble)
4) p(a black marble then a green marble)
5) p(two marbles that are not red)
6) p(two marbles that are neither blue nor green)

7) a family has two children, both of whom are boys. what is the probability that the next child will be born a boy?

Answer 1

Hi! First understand the sample space - all possibilities.

Answer 2

Sample space equals 8 green + 5 red + 4 blue + 3 black = 20. This will always be the denominator of the probability. remember, probability is:

Desired Outcome/All Outcome

Answer 3

two black marbles means
1) first is black and
2) second is black given that the first is black
multiply these two probabilities together
first is black \(\frac{3}{20}\)
second is black given that the first is black \(\frac{2}{19}\)

your answer
\[\frac{3}{20}\times \frac{2}{19}\]

Answer 4

not to be argumentative, but 20 is not always the denominator

Answer 5

Yes, I agree. But this is assuming we are only picking one marble. I understand, without replacement, the denominator decreases :)

Answer 6

thats the part im confused at

Answer 7

For part 1:
Two green marbles means a green marble on the first try AND a green marble on the second try.

Answer 8

@helpmeplease123123 is it clear how i solved number two? because the others are similar

Answer 9

Since there is an "and" involved, we use the multiplication principle of probability.
P(2 green) = P(1 green 1st try)*P(1 green 2nd try)

Answer 10

im lost still :(

Answer 11

first is black \(\frac{3}{20}\) because there are 3 black and 20 in total
now given that the first one is black, there are only 2 black ones left, and only 19 total
so the probability that the second one is black given that the first one is black is \(\frac{2}{19}\)

Answer 12

so for 1) is 1 over 19

Answer 13

For part 1: Two green marbles means a green marble on the first try AND a green marble on the second try.
Since there is an "and" involved, we use the multiplication principle of probability. P(2 green) = P(1 green 1st try)*P(1 green 2nd try)
There are 8 green marbles.
First try probability:
P(1 green 1st try) = Desired/Total = (8 green)/(20 total) = 2/5
Now, there are only 19 marbles left since 1 green is gone.

Answer 14

so the probability that both are black is the product of those two probabilities
\[\frac{3}{20}\times \frac{2}{19}\]

Answer 15

soo 1 over 19 ?

Answer 16

p(1 green 2nd try) = desired/total = 7 green/19 total = 7/19
Final probability equals (2/5)*(7/19)=15/85=3/17

Answer 17

oooo thanks

Answer 18

This is for number 1. The rest are similar. Take a look at mine and satellite's solution for #1 and #2.

Answer 19

No problem!

Answer 20

i still need help with the rest