A bag contains 8 red marbles, 2 white marbles, and 6 blue marbles. A marble is picked at random and is replac

Question

A bag contains 8 red marbles, 2 white marbles, and 6 blue marbles. A marble is picked at random and is replaced. Then a second marble is picked at random. Find the probability first marble is red and the second marble is not blue.

Answer 1

The probability of any marble to be picked is 16/16=1.
The probability of a red marble to be picked first is

P(red)=8/16=1/2=0.5

Since the marbles are replaced ones picked their total number is still 16 and their probabilities for being picked continue to be the same.

Now we can compute the probability of the second marble is not blue is

P(not blue)=8/16+2/16=5/8 = 0.625
or
P(not blue)=(1-P(blue))=
=1-6/16=(16-6)/16=5/8

Answer 2

You have a total of 16 marbles in the bag. Half are red so you have a 50% chance of picking red. Since there is only 6 blue total you will formulate the fraction 6/16. Now you can break down the common factor of 2 to get 3/8.

Sorry, misread the question...since there are 6 that are blue there are then that are not...so that fraction would be 10/16 or 5/8

Answer 3

In the experiment piking a marble from a bag containing 16 marbles (8 red marbles, 2 white marbles, and 6 blue marbles)

Let 'A' be the event of getting the marble is a red and
Let 'B' be the event of getting the marble is not a blue.

Totla number of possible choices = Number of ways in which one marblel can be drawn from totle of 16 marbles

==> n = 16 C 1
==> n = 16

For event 'A'
-----------------
Number of favourable choices = Number of ways in which one marble can be drawn from 8 red balls

==> m = 8 C 1
==> m = 8

Probability of occurance of event 'A' = Number of favourable choices for event 'A' / Total number of possible choices

==> P(A) = m / n
==> P(A) = 8 / 16
==> P(A) = 1 / 2

Therefore P(A) = 1 / 2

For event 'B'
-----------------
Number of favourable choices = Number of ways in which one marble can be drawn from 10 marbles i.e 8 red and 2 white marbels

==> m = 10 C 1
==> m = 10

Probability of occurance of event 'B' = Number of favourable choices for event 'B' / Total number of possible choices

==> P(B) = m / n
==> P(B) = 10 / 16
==> P(B) = 5 / 8

Therefore P(B) = 5 / 8

Note:- Both the events A and B are independent events i.e the probablity of occurance of an event A is not depends upon the probability of occurance of an event B

Now Probability of occurance of both the events 'A' and 'B' are

P('A' intersection 'B') = P(A) x P(B)
= 1 / 2 x 5 / 8
= 5 / 16
Therefore the probebility of occurance of picking first marble is red and second marble is not a blue is 5/16

Note:- In this problem marbles are replaced at each time when they drawn, so total number of marbles in the box are 16 at any instant and total number of possible choices are same for both the events.


For more detailes and better understanding:

http://www.futureaccountant.com/probability/

http://www.schoolingkids.com/probability/

Answer 4

8 red marbles
2 white marbles
6 blue marbles

16 total marbles

There are two events:

1)You pick a marble out of a bag of 16 marbles
2) (you replace that marble) You pick a marble out a bag of 16 marbles

The two events are "independent" because the outcome of the first event doesn't influence the outcome of the second event. That is because you replaced the first marble you picked.

The probability of two independent events equals the product of the probabilities of each event.

P(Total) = P(1) * P(2)

P(1) = 8 red / 16 total marbles = 1/2
P(2) = (2 white + 8 red) / 16 total marbles (not a blue marble)
= 10/16 = 5/8

P(Total) = (1/2)*(5/8) = 5/16

Answer 5

There are 16 marbles in total. So
1) prob of marble being red is 8/16 (or 1/2 or 50%)
2) prob of marble being not blue is 10/16 (or 5/8)

Answer 6

Total number of marbles: 16

Probability first marble is red: 8/16, or 1/2 (50%)

Probability second marble is not blue: 10/16, or 5/8 (62.5%)

Answer 7

1) 8/16= 1/2
2) 10/16

Answer 8

50% chance it's red and because it's been placed back in the bag, the probability of blue remains at 37.5%...I'm certain I'm wrong but what the hell, why not give it a shot.

Answer 9

The first pick is 50% and the second pick is 62.5% so the answer is 31.25%.