Question

Un dado ordinario (regular) es un cubo con los números del 1 al 6 en los lados (representado por puntos pintados). Imaginemos que tal dado sea lanzado dos veces en sucesión y que los valores de las caras en los dos lances son sumados. Esta suma se registra como el resultado de un único ensayo de un experimento aleatorio. Calcular la probabilidad de cada uno de los siguientes sucesos: Suceso A: La suma es mayor que 7. Suceso B: La suma no es divisible entre 3 y no es divisible entre 4.

Answer 1

To find the probability of rolling a sum greater than 7 with two dice (Event A), count the favorable outcomes (21/36 or 7/12 probability). For the probability of rolling a sum not divisible by 3 or 4 (Event B), eliminate divisible by 3 and 4 cases from total outcomes to find there are 18 favorable outcomes out of 36, resulting in a 1/2 probability.

Step-by-step explanation:

Probability of Rolling a Dice

When rolling a fair six-sided die twice, there are 36 possible outcomes (6 options for the first roll × 6 options for the second roll). To calculate the probability of Event A (the sum greater than 7), we count the outcomes where the sum of the two dice is greater than 7 and then divide by the total number of outcomes. There are 21 such outcomes (for example, 2+6, 3+5, 4+4, and so on), leading to a probability of 21/36 or 7/12 after simplification.

For Event B (the sum is not divisible by 3 or 4), we need to eliminate all sums divisible by 3 and 4 from the possible outcomes and count the remaining ones. There are 12 outcomes where the sum is divisible by 3 (e.g., 1+2, 2+1, 3+3), and 9 outcomes where the sum is divisible by 4 (e.g., 2+2, 3+1, 4+4). However, we must be careful not to double-count the outcomes that are divisible by both 3 and 4 (e.g., 3+3), therefore the total count of outcomes that satisfy Event B is 36 - 12 - 9 + 3 = 18, giving us a probability of 18/36 or 1/2 after simplification.

Answer 2

• The probability of event A is 5/12.
• The probability of event B is 13/36.

How to find the probability?

There are a total of 36 possible outcomes for two dice, since each die has 6 possible outcomes. The outcomes that result in a sum greater than 7 are:

(6,6)

(6,5)

(6,4)

(6,3)

(6,2)

(5, 6)

(5, 5)

(5, 4)

(5, 3)

(4, 6)

(4, 5)

(4, 4)

(3, 6)

(3, 5)

(2, 6)

There are 15 possible outcomes that satisfy this condition, so the probability of event A is:

P(A) = 15/36 = 5/12

Event B: The sum is not divisible by 3 or 4

The outcomes sums that aren't divisible by 3 or 4 are:

(1, 1)

(1, 4)

(1, 6)

(2, 3)

(2, 5)

(3, 2)

(3, 4)

(4, 1)

(4, 3)

(5, 2)

(5, 6)

(6, 1)

(6, 5)

P(B) = 13/36