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aleksandrvk [35]
3 years ago
13

As every Girl Scout knows, statistics teachers seriously love Girl Scout Cookies. The number of boxes of GS cookies statistics t

eachers order, like all important decisions made by statistics teachers, is determined by independent rolls of a 4-sided fair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxes are ordered.
a) What is the probability that a statistics teacher places an order for 2 boxes of Girl Scout cookies?
b) What is the probability that with two independently chosen statistics teachers will each order 6 boxes each?
c) What is the probability that for two independently chosen statistics teachers the first will order 6 boxes and the second will order 2 boxes?
d) What is the probability that for two independently chosen statistics teachers exactly one will order 6 boxes?
Mathematics
1 answer:
Alexandra [31]3 years ago
4 0

Answer:

a) 0.75

b) 0.0625

c) 0.1875

d) 0.375

Step-by-step explanation:

Let's start by first finding the probability a teacher orders 6 boxes. Since it is a four sided dice, the probability of getting a 1 is going to be 0.25.

Similarly, for any other number on the dice, the teacher orders 2 boxes. We can think of this as NOT rolling a 1. Using our previous answer, this comes out to be: 1 - 0.25 = 0.75

It should be remembered in the following answers that teachers ordering 6 or 2 boxes are not influenced by the results of other teachers. These are statistically independent events.

a) As given above, this probability is 0.75

b) The probability that both teachers order 6 boxes will be their individual probabilities multiplied. This comes out to be: 0.25 x 0.25 = 0.0625

c) Like in part (b), this is both of their probabilities multiplied:

   0.25 x 0.75 = 0.1875

d) This is nearly the same as part (c), but with a little twist. The order matters. There are two scenarios:

  1.   First teacher gets 6 boxes, and the second gets 2.
  2.   First teacher gets 2 boxes, and the second gets 2.

Both of these events have a probability of 0.1875, as shown in (c). To get the total probability of this event happening, we must add these together:

0.1875 + 0.1875 = 0.375

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