Respuesta :
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: P(AUB) = [tex]\frac{2}{9}[/tex]
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) = [tex]\frac{6}{36} + \frac{3}{36} - \frac{1}{36}[/tex]
P(AUB) = [tex]\frac{8}{36}[/tex]
P(AUB) = [tex]\frac{2}{9}[/tex]
The probability, using the general addition rule, is P(AUB) = [tex]\frac{2}{9}[/tex]
