supposed that two balanced dice are rolled. let Y denote the product of the two numbers. use random variable notation to represent the event that the product of the two numbers is greater than 4
a {5,6}
b {XY>4}
c{Y>4}
d P(Y>4)
wait just kidding, its already noted that Y is the product, so it would be C, my bad.
I would go with B. It's the only choice that states the product is greater than 4.
The correct answer is option b) {XY > 4}.
In random variable notation, the event that the product of the two numbers is greater than 4 is represented as {XY > 4}.
Option a) {5,6} represents the event of rolling both dice and getting a 5 and a 6.
Option c) {Y > 4} represents the event of getting a product greater than 4 but does not specifically mention the dice outcome.
Option d) P(Y > 4) represents the probability of the event {Y > 4}, which is not given in the question.
So, the correct representation of the event that the product of the two numbers is greater than 4 is option b) {XY > 4}.
The correct random variable notation to represent the event that the product of the two numbers is greater than 4 is:
b {XY>4}
To calculate the probability of this event occurring, you need to determine the sample space (all possible outcomes) and the favorable outcomes (outcomes that satisfy the condition).
The sample space for rolling two balanced dice is given by S = {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}, where each pair represents the two numbers rolled on the dice.
To find out the favorable outcomes for XY > 4, we need to list all the pairs of numbers that have a product greater than 4. These include:
(3,3), (3,4), (3,5), (3,6),
(4,3), (4,4), (4,5), (4,6),
(5,3), (5,4), (5,5), (5,6),
(6,3), (6,4), (6,5), (6,6).
Therefore, the favorable outcomes are F = {(3,3), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}.
The probability of Y > 4 can be calculated using the formula P(Y > 4) = |F| / |S|, where |F| denotes the number of favorable outcomes and |S| denotes the total number of outcomes in the sample space.
Substituting the values, we have:
P(Y > 4) = |F| / |S| = 16 / 36 = 4 / 9.
Therefore, the correct answer is:
d P(Y > 4) = 4 / 9.