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ycow [4]
3 years ago
13

A bag contains 7 red marbles, 3 blue marbles and 2 green. If two marbles are drawn out of the bag, what is the probability, to t

he nearest 1000th, that both marbles drawn will be blue?
Mathematics
1 answer:
Setler [38]3 years ago
5 0

Answer:

0.0455

Step-by-step explanation:

<u>The formula for calculator probability is </u>

# of favorable outcomes / # of possible outcomes

<u>The total number of marbles in the bag: </u>

7+3+2=12

<u>Probability of the first marble being blue:</u>

3/12

<u>Probability of the second marble being blue:</u>

2/11 -- 2 because only 2 blue marbles left after drawing the first one out, 11 because after taking the first marble out, we have 11 marbles left in the bag

<u>Formula for both events happening:</u>

p(A and B) = p(A) * p(B)

In this problem,

A = first one blue

B = second one blue

<u>Probability that if two marbles are drawn out of the bag, both are blue:</u>

3/12 x 2/11 = 0.045454

<u>Rounded answer:</u>

0.0455 (or 4.55%)

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Answer:

The mentioned number in the exercise is:

  • <u>362</u>

Step-by-step explanation:

To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.

If:

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  • y = tens digit
  • z = ones digit

We can write:

  1. x = z + 1 (the hundreds digit is one more than the ones digit).
  2. y = 2x (the tens digit is twice the hundreds digit).
  3. x + y + z = 11 (the sum of the digits is 11).

Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:

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  • (z + 1) + y + z = 11 (remember x = z + 1)
  • z + 1 + y + z = 11
  • z + z +y + 1 = 11 (we just ordered the equation)
  • 2z + y + 1 = 11 (z + z = 2z)
  • 2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
  • 2z + y = 10
  • 2z + (2x) = 10 (remember y = 2x)
  • 2z + 2x = 10
  • 2z + 2(z + 1) = 10 (x = z + 1 again)
  • 2z + 2z + 2 = 10
  • 4z + 2 = 10
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  • 4z = 8
  • z = 8/4
  • <u>z = 2</u>

Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:

  • x = z + 1
  • x = 2 + 1
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And we'll use the second equation to obtain the value of y (the tens digit):

  • y = 2x
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Organizing the digits, we obtain the number:

  • Number = xyz
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As you can see, <em><u>the obtained number is 362</u></em>.

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