A jar contains 6 chocolate chip cookies and 9 peanut butter cookies. Richard grabs 3 cookies at random to pack in his lunch. What is the probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie?

Answers

Answer 1

Answer: The answer is 0.096.

To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur.

There are in total 15 cookies in the jar:
6 chocolate chip cookies + 9 peanut butter cookies = 15 cookies

The probability to drew 1 chocolate chip cookie is: $P_1= (6)/(15) = (2)/(5)$
The probability to drew 1 peanut butter cookie is: $P_2= (9)/(15) = (3)/(5)$

In this example, we have three events occurring together:
1. The probability that he drew 1 chocolate chip cookie: $P_1= (2)/(5)$
2.The probability that he drew 1 chocolate chip cookie: $P_1= (2)/(5)$
3. The probability that he drew 1 peanut butter cookie: $P_2= (3)/(5)$

By using the multiplication rule, the probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie is 0.096:
$P=P_1*P_1*P_3= (2)/(5) * (2)/(5) * (3)/(5) = (2*2*3)/(5*5*5) = (12)/(125) = 0.096$

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Solve the following system of equations for all three variables.5x−2y+z = 8
−9x+2y+2z = 5
−9x−2y−5z = 4

Answers

  5x - 2y + 1z = 8 ⇒   5x - 2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9x - 2y - 5z = 4 -4x + 3z = 13

5x - 2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9z - 2y - 5z = 4 ⇒ -9x - 2y - 5z = 4
-18x - 3z = 9

-4x + 3z = 13
  -18x - 3z =   9
-22x = 22
  -22 -22
  x = -1
  -18x - 3z = 9
-18(-1) - 3z = 9
18 - 3z = 9
- 18 - 18
-3z = -9
-3 -3
z = 3

5x - 2y + z = 8
5(-1) - 2y + 3 = 8
-5 - 2y + 3 = 8
-2y - 5 + 3 = 8
-2y - 2 = 8
  + 2 + 2
  -2y = 10
-2   -2
y = -5
  (x, y, z) = (-1, -5, 3)

Plot the following points on the grid and calculate the slope of the line that passes through them (-2, -3) and (4, 5): a) 1 b) 2 c) 3 d) 4"