Question 1177120: a. A blue marble is drawn.
b. A red marble is drawn.
c. A red or green marble is drawn.
d. A blue and then a green marble is drawn with replacement.
e. A blue and then a green marble is drawn without replacement.
f. Two green marbles are drawn with replacement.
g. A green marble is drawn.
h. A red or blue marble is drawn.
match these to the above questions!
i. 9/29 x 7/28
ii. 7/29
iii. 13/29
iv. 7/27 x 7/29
v. 9/29 x 7/29
vi. 13/29 + 9/29
vii. 9/29
viii. 13/29 + 7/29
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
a. A blue marble is drawn. P = 9/29 vii
b. A red marble is drawn. P=13/29 iii
c. A red or green marble is drawn. 13/29 + 7/29 viii
d. A blue and then a green marble is drawn with replacement. (9/29)(7/29) v
e. A blue and then a green marble is drawn without replacement. (9/29)(7/28) i
f. Two green marbles are drawn with replacement. P = (7/29)(7/29) iv
g. A green marble is drawn. P = 7/29 ii
h. A red or blue marble is drawn. 13/29 + 9/29 vi
Wish You the Best in your Studies.
Answer by greenestamps(13330)  (Show Source):
You can put this solution on YOUR website!
On first reading the problem, I thought we had to be told how many of each colored marble there are in the bag to start with. However, we can use logical reasoning to determine that information to solve the problem.
There are many paths to the solution; here is what I think is probably the fastest.
i. is the only calculation in which the denominator of the second fraction indicates drawing two marbles without replacement. Since e. is the only scenario in which that is done, the calculation 9/29 * 7/28 tells us that there are 9 blue marbles and 7 green marbles in the bag; and so there are 13 red marbles.
Knowing the numbers of each color marble in the bag, the matching is then easy.
Note that OR indicates a single action is occurring; the probabilities get added, and the denominators of the two probabilities must both be 29.
And similarly note that AND indicates two actions are occurring one after the other; the probabilities get multiplied. If the two actions are with replacement, the two denominators are both 29; if they are without replacement, the first denominator is 29 and the second is 28.
Based on those requirements, calculations iv. does not make any sense; the only time you would have a denominator 27 is if a third marble were being drawn without replacement. That might be an error in the statement of the problem; or it might be intentional to see if the student realizes they don't make sense.
i. 9/29 * 7/28 --> blue AND then green, without replacement --> e.
ii. 7/29 --> green --> g.
iii. 13/29 --> red --> b.
iv. impossible...
v. 9/29 * 7/29 --> blue AND the green, with replacement --> d.
vi. 13/29 + 9/29 --> red OR blue --> h.
vii. 9/29 --> blue --> a.
viii. 13/29+7/29 --> red OR green --> c.
Note scenario f. was not used; it is two green marbles with replacement. That calculation would be 7/29 * 7/29; so I will guess the "7/27" in iv. is a typo....
|
|
|
