Consider the experiment of drawing two cards from a

deck in which all picture cards have been removed and
adding their values (with ace = 1).

a. Describe the outcomes of this experiment. List the
elements of the sample space.
b. What is the probability of obtaining a total of 5 for
the two cards?
c. Let A be the event “total card value is 5 or less.”
Find P ( A ) and P ( Ac)

a. To describe the outcomes of the experiment, we need to determine all possible combinations of cards that can be drawn. Since the picture cards have been removed, we are left with only numbered cards and the Ace.

The numbered cards have values from 2 to 10, and the Ace has a value of 1. So, the possible outcomes for the two cards can be represented by pairs of numbers between 1 and 10, inclusive.

The sample space, which consists of all possible outcomes, can be listed as follows:
{(1,1), (1,2), (1,3), ..., (1,10),
(2,1), (2,2), (2,3), ..., (2,10),
...
(10,1), (10,2), (10,3), ..., (10,10)}

b. To find the probability of obtaining a total of 5 for the two cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are:
{(1,4), (2,3), (3,2), (4,1)}

There are 4 favorable outcomes, and the total number of outcomes is 100 (since there are 10 choices for each of the two cards). Therefore, the probability is:

P(total of 5) = favorable outcomes / total outcomes
P(total of 5) = 4/100
P(total of 5) = 0.04

So, the probability of obtaining a total of 5 for the two cards is 0.04 or 4%.

c. Let A be the event "total card value is 5 or less." To find P(A), we need to determine the number of outcomes that satisfy the event A and divide it by the total number of possible outcomes.

The outcomes that satisfy the event A are:
{(1,1), (1,2), (1,3), (1,4),
(2,1), (2,2), (2,3), (2,4), (2,5),
(3,1), (3,2), (3,3), (3,4), (3,5),
(4,1), (4,2), (4,3), (4,4), (4,5),
(5,1), (5,2), (5,3), (5,4), (5,5)}

There are 25 outcomes that satisfy the event A, out of a total of 100 possible outcomes. Therefore, the probability is:

P(A) = outcomes satisfying A / total outcomes
P(A) = 25/100
P(A) = 0.25

So, the probability of event A (total card value is 5 or less) occurring is 0.25 or 25%.

To find P(Ac), the probability of the complement of event A (i.e., the event not A or "total card value is greater than 5"), we subtract the probability of A from 1:

P(Ac) = 1 - P(A)
P(Ac) = 1 - 0.25
P(Ac) = 0.75

So, the probability of event Ac (total card value is greater than 5) occurring is 0.75 or 75%.