Let the probability experiment be to roll two fair dice a single time and observ

ID: 3048878 • Letter: L

Question

Let the probability experiment be to roll two fair dice a single time and observe the “pips” (dots) on the upturned faces. The sample space is described below. The fact that some of the ordered pairs are red becomes evident in (A) below.

Let (x,y) = (pips on die 1, pips on die 2)

PIPS ON DIE 1

1 2 3 4 5 6

1 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

2 (1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

3 (1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

PIPS ON DIE 2 4 (1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

5 (1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

a. P(product of the pips is at most 6)

b. P(sum of the pips is at least 10)

c. P(sum of the pips is exactly 7)

d. P(product of the pips is a odd number)

e. P(product of the pips is a multiple of 6)

f. P(sum of the pips is at least 2)

PLEASE SHOW ALL WORK

Explanation / Answer

Solution

(a) p(product of the pips is at most 6)

Product can be = 1,2,3,4,5,6

P(product is 1) = 1/36

P(product =2) = 2/36

P(product =3) = 2/36

P(product =4) = 3/36

P(product =5) = 2/36

P(product =6) = 4/36

Sum = 14/36 = 7/18

(b) P(sum of the pips is at least 10) = samplespace = ((6,4),(5,5),(6,5),(4,6)(5,6),(6,6)) = 6/36 = 1/6

(d) P(product of the pips is a odd number) = ((1,1)(3,1)(5,1),(1,3),(3,3)*5,3),(1,5),(3,5),(5,5)) = 9/36 = 1/4

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Let the probability experiment be to roll two fair dice a single time and observ

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