## anonymous one year ago A bag has 1 red marble, 4 blue marbles, and 3 green marbles. Peter draws a marble randomly from the bag, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.

1. Valpey

Multiply the probability of drawing just one blue marble times itself.

2. anonymous

wait. So 1*4?

3. Valpey

The probability of drawing one blue marble is equal to the fraction: number of blue marbles over the total number of marbles.

4. Valpey

Which is more likely, drawing a blue marble or flipping a coin and getting tails?

5. anonymous

drawing a blue marble i am assuming because there is only one side that has tails when there are four different blue marbles.

6. anonymous

what am multiplying exactly though besides the one marble? The mean times the one marble? the fraction would be 4/8 or simplified to 1/2

7. anonymous

@Valpey @Hero

8. Valpey

Right 1/2 or 50% of the time you draw a blue marble.

9. Valpey

What percent of the time do you draw a blue marble twice in a row? (same as getting tails in two coin tosses)

10. anonymous

thats the part I am confused about.

11. Valpey

If I flip a coin twice, what is the chance it comes tails, tails?

12. anonymous

it could be HH TT or TH. so I would say 1/3 or a chance...

13. anonymous

of*

14. anonymous

I am so confused @Valpey

15. Valpey

You left out HT which is just as likely as TH. So the four equally likely outcomes are: HH, TH, HT, TT Similarly let's say B for Blue Marble and N for Not Blue Marble. The four equally likely outcomes are: BB, BN, NB, NN

16. anonymous

ohhhhhh okay

17. anonymous

But how does that go along with the problem? hehe sorry im slow

18. anonymous

@Valpey

19. Valpey

The answers are the same. Blue marbles represent 50% of the marbles so drawing one is equivalent to any other 50:50 outcome, like tossing a coin.

20. Valpey

The chance of drawing two Blue Marbles in a row (with replacement) is the same as the chance of flipping a coin twice and getting tails, tails. This happens 1 in 4 times or 25%.

21. Valpey

But we can change the problem slightly and see better how to extend this. Suppose instead there are 3 Blue Marbles and 5 Not Blue Marbles. Now we still have four possible outcomes: BB, BN, NB, NN but now they are not all equally likely. Each outcome is the product of the chance of the two independent events separately. BB = $$\frac{3}{8}*\frac{3}{8} =\frac{9}{64}$$ BN = $$\frac{3}{8}*\frac{5}{8} =\frac{15}{64}$$ NB = $$\frac{5}{8}*\frac{3}{8} =\frac{15}{64}$$ NN = $$\frac{5}{8}*\frac{5}{8} =\frac{25}{64}$$

22. anonymous

OHHHHHhhhhhhhhhhhHHHHHHHHhhhhhhhHHHHHHHhhhH