Question

Today there is a 60% chance of rain, a 30% chance of lightning, and a 15% chance of lightning and rain together. Determine if rain today and lightning today are independent events? A) The two events are independent because P(lightning) ⋅ P(rain) = 0.15 does not equal P(lightning and rain) = 0.18. B) The two events are not independent because P(lightning) ⋅ P(rain) = 0.15 does not equal P(lightning and rain) = 0.18. C) The two events are independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15 D) The two events are not independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15

Answer 1

Answer:

D. The two events are not independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15

Step-by-step explanation:

Since, two events A and B are independents,

If the occurrence does not affect the occurrence of other,

Mathematically,

P(A and B) = P(A) × P(B),

Here,

P(Rain) = 60% = 0.6,

P(Lightning) = 30% = 0.30,

P(lightning and rain) = 0.15,

∵ 0.15 ≠ 0.6 × 0.30 = 0.18

⇒ P(lightning and rain) ≠ P(Rain) × P(lightning),

Thus, the two events are not independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15