Slips of paper marked with the numbers 9, 10, 11, and 12 are placed in a box. After being mixed, two slip are drawn simultaneously. Write out the sample space S, choosing an S with equally like. Finally , write the indicated events below in set notation.
a. Both slips are marked with even numbers.
b.One slip is marked with an odd number and the other is marked with an even number.
c.Both slips are marked with the same number.
Solution:-
The sample space is the set of all people slips of paper. The order of the slips of paper does not matter. Use the number on each slip of paper to write the events.
To write the sample space, list all different possible combinations of two different numbers.
S = {(9,10), (9,11), (9,12),(10,11),(10,12),(11,12)}
The value of n(S) is the number of outcomes in the sample space,
S = {(9,10), (9,11), (9,12),(10,11),(10,12),(11,12)}
n(S) = 6
The numbers are all equally likely to be chosen, so the sample space has equally likely outcomes.
a. Write the event both slips are marked with even numbers. The sample space is show below. List all the outcomes from the sample space where both slips are marked with even number.
S = {(9,10), (9,11), (9,12),(10,11),(10,12),(11,12)}
The event is the set of outcomes that have both slips marked with an even number. Based on the sample space, the event is {(10,12)}.
b. Write the event both slips are marked with even numbers. The sample space is shown below.
S = {(9,10), (9,11), (9,12),(10,11),(10,12),(11,12)}
The event is the set of outcomes that have both an odd number and an even number. Based on the sample space, the event is {(9,10), (9,12),(11,10),(11,12)}.
c. Write the event both slips both slips are marked with the same number. The sample space is shown below.
S = {(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)}
The event is the set of outcomes that have same number twice. There are no outcomes in the sample space that have the same number twice. Therefore, the event is the empty set, ø.