Respuesta :
The correct answer for the question that is being presented above is this one: "d. 2/5." John is playing a game of darts. The probability that he throws a dart into the center of the dart board (the Bull’s eye) is 1/10. The probability that he throws the dart into the 10-point ring is 3/10. The probability that he either hits a Bull's eye or scores 10 points is 2/5
Answer: The correct option is (d). [tex]\dfrac{2}{5}.[/tex]
Step-by-step explanation: Given that John is playing a game of darts. The probability that he throws a dart into the centre of the dart board (the Bull’s eye) is [tex]\dfrac{1}{10}[/tex] and the probability that he throws the dart into the 10-point ring is [tex]\dfrac{3}{10}.[/tex]
We are to find the probability that he either hits a Bull’s eye or scores 10 points.
Let, 'A' and 'B' represents the events that John throws the dart into a Bull's eye and 10-point ring respectively.
Then, according to the given information, we have
[tex]P(A)=\dfrac{1}{10},~~P(B)=\dfrac{3}{10},~~~P(A\cup B)=?[/tex]
Since John cannot throw the dart into the Bull's eye and 10 point ring together, both the events are independent of each other.
Therefore,
[tex]P(A\cap B)=0[/tex]
From the theorems of probability, we have
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=\dfrac{1}{10}+\dfrac{3}{10}-0=\dfrac{4}{10}=\dfrac{2}{5}.[/tex]
Therefore, the probability that John either hits a Bull’s eye or scores 10 points is [tex]\dfrac{2}{5}.[/tex]
Thus, (d) is the correct option.
