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Alejandro surveyed his classmates to determine who has ever gone surfing and who has ever gone snowboarding. let a be the event that the person has gone surfing, and let b be the event that the person has gone snowboarding. a 4-column table has 3 rows. the first column has entries has surfed, never surfed, total. the second column is labeled has snowboarded with entries 36, 12, 48. the third column is labeled never snowboarded with entries 189, 63, 252. the fourth column is labeled total with entries 225, 75, 300. which statement is true about whether a and b are independent events? a and b are independent events because p(a∣b) = p(a) = 0.16. a and b are independent events because p(a∣b) = p(a) = 0.75. a and b are not independent events because p(a∣b) = 0.16 and p(a) = 0.75. a and b are not independent events because p(a∣b) = 0.75 and p(a) = 0.16.

Respuesta :

Using the concept of independent events, it is found that the correct statement is:

a and b are independent events because p(a∣b) = p(a) = 0.75.

When are two events independent?


Two events, A and B, are independent if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, the events are:

  • Event A: Surfing.
  • Event B: Snowboarding.

In this problem, out of 300 students, 225 have surfed, hence:

[tex]P(A) = \frac{225}{300} = 0.75[/tex]

48 have gone snowboarding, hence:

[tex]P(B) = \frac{48}{300} = 0.16[/tex]

36 have done both, hence:

[tex]P(A \cap B) = \frac{36}{300} = 0.12[/tex]

The multiplication is:

P(A)P(B) = 0.75 x 0.16 = 0.12.

That is, the probability of A given B is P(A|B) = P(A) = 0.75, hence they are independent.

More can be learned about independent events at https://brainly.com/question/14478923

BelvaB

Answer:

the answer is B

Step-by-step explanation:

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