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).
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)
Liked your answer, did not see it the first time, thanks!
This can't be correct. There are four suits so wouldn't the sample space be 45 x 4 = 180??
A. To describe the outcomes of this experiment, we need to consider the values of the cards that can be drawn. In this deck, there are only cards with values from 1 to 10. We draw two cards and add their values to get a total. The sample space consists of all possible combinations of two cards from the deck.
The elements of the sample space can be listed as follows:
{(1,1), (1,2), (1,3), ..., (1,10)}
{(2,1), (2,2), (2,3), ..., (2,10)}
{(3,1), (3,2), (3,3), ..., (3,10)}
...
{(10,1), (10,2), (10,3), ..., (10,10)}
There are a total of 100 possible outcomes in the sample space.
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.
The favorable outcomes in this case are the combinations that sum up to 5. These combinations are: (1,4), (2,3), and (3,2). So, there are three favorable outcomes.
The probability of obtaining a total of 5 is given by:
P(total of 5) = favorable outcomes / total outcomes = 3 / 100 = 0.03 (or 3%)
C. Let A be the event "total card value is 5 or less." To find P(A), we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
The favorable outcomes for event A include all combinations that have a total value of 5 or less. These combinations are: (1,1), (1,2), (1,3), (2,1), (2,2), (3,1).
So, there are six favorable outcomes.
The probability of event A, P(A), is given by:
P(A) = favorable outcomes / total outcomes = 6 / 100 = 0.06 (or 6%)
To find P(Ac), which is the probability of the complement of event A (not event A), we subtract P(A) from 1:
P(Ac) = 1 - P(A) = 1 - 0.06 = 0.94 (or 94%)