Respuesta :
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Let A and B represent the following events.
A = At least one of a pair of fair dice lands of 5
B = Sum of the dice is 7
It two dice are rolled then total number of outcomes is 36.
A = {(1,5),(2,5),(3,5),(4,5),(5,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6)} = 11
B= {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}=6
A∩B = {(2,5),(5,2)}=2
[tex]P(A)=\dfrac{11}{36},P(B)=\dfrac{6}{36},P(A\cup B)=\dfrac{2}{36}[/tex]
We need to find the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7.
[tex]P(A|B)=\dfrac{P(A\cup B)}{P(B)}[/tex]
[tex]P(A|B)=\dfrac{\dfrac{2}{36}}{\dfrac{6}{36}}[/tex]
[tex]P(A|B)=\dfrac{2}{6}[/tex]
[tex]P(A|B)=\dfrac{1}{3}[/tex]
Therefore, the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7 is 1/3.
The probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7 is 1/3.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
We know that the sum of the dice is already 7, therefore, the possible options that the sum of fair dice is 7 are,
S = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
Now, we need that one of the two dice must give 5 as the output, therefore, the possible options are,
N = {(2,5), (5,2)}
As we know the formula for finding the probability, therefore, substitute the values,
[tex]\rm Probability(\text{One of the dice gives 5}) = \dfrac{Desired\ Outcomes\ n(S)}{Total\ Number\ of\ outcomes\ possible\ n(N)}[/tex]
[tex]\rm Probability(\text{One of the dice gives 5}) = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
Hence, the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7 is 1/3.
Learn more about Probability:
https://brainly.com/question/795909
