Consider the experiment of drawing two cards from a deck in which all pictures 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).
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A. In this experiment, we are drawing two cards from a deck, excluding picture cards, and adding their values. The elements of the sample space can be represented by a combination of possible card values for the first card and the second card.
The possible card values are: 1 (ace), 2, 3, 4, 5, 6, 7, 8, 9, 10. Since we are drawing two cards, each value can be paired with other values from the list. For example, if the first card is a 2, the second card can be any value from 1 to 10. Similarly, if the first card is a 3, the second card can be any value from 1 to 10, except 3 because that would result in a picture card, which is excluded.
Therefore, the sample space can include pairs of values like (1,1), (1,2), (1,3), ..., (10,10), where each element represents a possible outcome of this experiment.
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 for obtaining a total of 5 are as follows:
(1,4), (2,3), (3,2), (4,1).
The total number of possible outcomes is the number of elements in the sample space, which is 10 (since there are 10 possible card values).
Therefore, the probability of obtaining a total of 5 for the two cards is 4/10 = 0.4.
C. Let A be the event "total card value is 5 or less."
To find P(A), we need to determine the number of favorable outcomes for event A and divide it by the total number of possible outcomes.
The favorable outcomes for event A would be pairs of values that result in a total card value of 5 or less. These are:
(1,1), (1,2), (1,3), (1,4),
(2,1), (2,2), (2,3),
(3,1), (3,2),
(4,1).
The number of favorable outcomes for event A is 10.
Therefore, P(A) = 10/10 = 1.
To find P(Ac) (the probability of the complement event of A), we subtract P(A) from 1:
P(Ac) = 1 - P(A) = 1 - 1 = 0.