Question

Find the indicated probability by using the general addition rule. When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 4.

Answer 1

Answer:

The probability that either doubles are rolled or the sum of the dice is 4

= (8/36) = (2/9) = 0.2222

Step-by-step explanation:

The total sample space = 36

For the probability that either doubles are rolled or the sum of the dice is 4.

The possible sample spaces for this event include

Doubles - (1,1) (2,2) (3,3) (4,4) (5,5) (6,6)

Sum of dice is 4 - (1,3) (2,2) (3,1)

The total possible spaces - (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) (1,3) (3,1) (the possible outcome (2,2) appears twice, So, it is written as one possible outcome)

The total number of these possible outcomes = 8

Total sample space = 36

the probability that either doubles are rolled or the sum of the dice is 4

= (8/36) = (2/9) = 0.2222

Hope this Helps!!!

Answer 2

Answer: P(AUB) = $\frac{2}{9}$

Step-by-step explanation: General Addition Rule states that the probability of two events is the sum of the probability of each event happening subtracted by the probability of both events happening, ie,

P(AUB) = P(A) + P(B) - P(A∩B)

Possibilities of doubles when two dice are rolled is: (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) or 6 possibilities in 36 possible outcomes.

P(A) = 6/36

Possibilities of the sum is 4 is: (1,3) (2,2) (3,1) or 3 possibilities in 36 outcomes.

P(B) = 3/36

One possibility is repeated in both: (2,2) . So,

P(A∩B) = 1/36

Using general addition rule

P(AUB) = P(A) + P(B) - P(A∩B)

P(AUB) = $\frac{6}{36} + \frac{3}{36} - \frac{1}{36}$

P(AUB) = $\frac{8}{36}$

P(AUB) = $\frac{2}{9}$

The probability, using the general addition rule, is P(AUB) = $\frac{2}{9}$