anonymous
  • anonymous
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.
Mathematics
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SOLVED
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katieb
  • katieb
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Valpey
  • Valpey
Multiply the probability of drawing just one blue marble times itself.
anonymous
  • anonymous
wait. So 1*4?
Valpey
  • Valpey
The probability of drawing one blue marble is equal to the fraction: number of blue marbles over the total number of marbles.

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More answers

Valpey
  • Valpey
Which is more likely, drawing a blue marble or flipping a coin and getting tails?
anonymous
  • anonymous
drawing a blue marble i am assuming because there is only one side that has tails when there are four different blue marbles.
anonymous
  • 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
anonymous
  • anonymous
@Valpey @Hero
Valpey
  • Valpey
Right 1/2 or 50% of the time you draw a blue marble.
Valpey
  • Valpey
What percent of the time do you draw a blue marble twice in a row? (same as getting tails in two coin tosses)
anonymous
  • anonymous
thats the part I am confused about.
Valpey
  • Valpey
If I flip a coin twice, what is the chance it comes tails, tails?
anonymous
  • anonymous
it could be HH TT or TH. so I would say 1/3 or a chance...
anonymous
  • anonymous
of*
anonymous
  • anonymous
I am so confused @Valpey
Valpey
  • 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
anonymous
  • anonymous
ohhhhhh okay
anonymous
  • anonymous
But how does that go along with the problem? hehe sorry im slow
anonymous
  • anonymous
@Valpey
Valpey
  • 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.
Valpey
  • 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%.
Valpey
  • 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 = \(\frac{5}{8}*\frac{5}{8} =\frac{25}{64}\)
anonymous
  • anonymous
OHHHHHhhhhhhhhhhhHHHHHHHHhhhhhhhHHHHHHHhhhH

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