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)
To represent the event that the product of the two numbers is greater than 4 using random variable notation, we can use the random variable Y to denote the product of the two numbers.
So, the random variable notation for the event that the product of the two numbers is greater than 4 would be:
b) {XY > 4}
Alternatively, we can also represent the event that the product of the two numbers is greater than 4 using another random variable Z, by considering only the product itself. In this case, the random variable notation would be:
c) {Z > 4}
As for calculating the probability that the product of the two numbers is greater than 4, we need to determine the sample space and the favorable outcomes.
The sample space consists of all the possible outcomes when rolling two balanced dice, and it will have a total of 36 outcomes (6 outcomes for the first die multiplied by 6 outcomes for the second die).
To find the favorable outcomes, we need to consider the products greater than 4, which are: 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, 6x1, 6x2, 6x3, 6x4, 6x5, 6x6. This gives us a total of 12 favorable outcomes.
Therefore, the probability of the product of the two numbers being greater than 4 would be:
d) P(Y > 4) = favorable outcomes / total outcomes = 12/36 = 1/3