There is a 62% chance that a painter will work today, a 32% chance that it will storm today, and a 20% chance of both happening. Determine whether the events a painter working today and a storm today are approximately independent events. Justify mathematically.

Approximately independent, because 0.32 ≠ 0.63
Not independent, because 0.32 ≈ 0.32
Approximately independent, because 0.32 ≈ 0.32
Not independent, because 0.32 ≠ 0.63

Question

There is a 62% chance that a painter will work today, a 32% chance that it will storm today, and a 20% chance of both happening. Determine whether the events a painter working today and a storm today are approximately independent events. Justify mathematically.

Approximately independent, because 0.32 ≠ 0.63
 Not independent, because 0.32 ≈ 0.32
 Approximately independent, because 0.32 ≈ 0.32
 Not independent, because 0.32 ≠ 0.63

Phantomdex · Answer

@toga

toga · Answer

To determine whether the events "a painter working today" and "a storm today" are approximately independent, we need to compare the probability of both events occurring together with the product of their individual probabilities.

P(painter works AND storm occurs) = 0.20

P(painter works) x P(storm occurs) = 0.62 x 0.32 = 0.1984

Since P(painter works AND storm occurs) is close to P(painter works) x P(storm occurs), we can say that these events are approximately independent.

Therefore, the answer is (c) Approximately independent, because 0.32 ≈ 0.32.