Question

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 probabilit 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).

Answer 1

sample space:
cards --- sum
1 2 --3
1 3-- 4
1 4 --5
1 5 --6
1 6 --7
1 7 --8
1 8 --9
1 9 -- 10
1 10 -- 11 total outcome here is 9 , one with a sum of 5

2 3 --5
2 4 -- 6
..
2 10 -- 12 total outcome here is 8 , one with a sum of 5

3 4
3 5
..
3 10 -- total outcomes here is 7, no sum of 5 possible

....

9 10 -- one outcome, no sum of 5

total number of outcomes:
9+8+7+6+5+4+3+2+1 = 45
cases where the sum is 5 is 2


B) prob of sum of 5 = 2/45

C) to get a sum of 5 or less, I see only 4 cases
prob (5 or less) = 4/45

don't know what you mean by P (Ac)

Answer 2

Liked your answer, did not see it the first time, thanks!

Answer 3

This can't be correct. There are four suits so wouldn't the sample space be 45 x 4 = 180??