Assessment 1. 2. 3. Let S= {1, 2, 3, 4, 5, 6}, E= {1, 3, 5}, F= {2, 4, 6} and 0= {2, 3}. Are the events F and G mutually exclusive? 0 A) yes B) no Let S= {1, 2, 3, 4, 5, 6}, E = {2, 4, 6}, F= {1, 3,...

Solutions
Solution: Given F = {2, 4, 6} and G = {2, 3}
Subsets F and G have 1 element in common. If the die shows 2, both events F and G will
have occurred at the same time and therefore F and G are not mutually exclusive.
Answer: B)
Solution: Given F = {1, 3, 5} and G = {3, 4}
Two events are described as complementary if they are the only two possible outcomes
and are mutually exclusive. Since there is another event E occurring and also there is a
common element in F and G, therefore F and G are not complementary.
Answer: A)
Solution: An event is any collection (subset) of outcomes contained in the sample space S. The
possible events are the subsets of {x, y, z}. A set with 3 elements has 2^3 = 8 subsets. The
empty set is a subset, and so is the whole set {x, y, z}.
Answer: A)
Solution: A sample space is a collection of all possible outcomes of a random experiment. If selecting
a card from standard deck of playing cards and noting whether the card is black or red, the
possible outcomes are black ‘B’ and red ‘R’.
Answer: D)
Solution: If selecting a card from standard deck of playing cards and noting whether the card is black
or red, the possible outcomes are black ‘B’ and red ‘R’. Therefore the sample space is
S = {B, R}. The events of the experiment are {Ø}, {B}, {R}, {B, R}.
Answer: D)
Solution: The event where a head is tossed when tossing a coin and an odd number is rolled when
rolling a die is {(H, 1), (H, 3), (H, 5)}
Answer: B)
Solution: A sample space is a collection of all possible outcomes of a random experiment. Here the
possibilities are that 1) both transistors are defective, 2) first transistor is defective and
second transistor is non-defective, 3) second transistor is defective and first transistor is
non-defective, 4) both transistors are non-defective. Therefore the sample space is
S = {dd, dn, nd, nn}
Answer: B)
Solution: A sample space is a collection of all possible outcomes of a random experiment. The
possible outcomes of...