Rain and the bus 3. To decide whether the rain and the bus running late are dependent or independent events, first define the two events and then write their probabilities as decimals. (3 points) Let event A = __. P(A) = . Let event B = . P(B) = . A and B = . P(A and B) = . 4. Use the probabilities from question 3 to decide whether the rain and the bus running late are independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)

Two events are said to be independent when the probability of one of the events happening does not in any way affect the probability of the other event happening, and vice versa.

Mathematically, independent events are related through the expression

P(A n B) = P(A) × P(B)

And the conditional expression P(A|B) or P(B|A) for independent events are given as

P(A|B) = P(A) And P(B|A) = P(B)

So, we check each of the mathematical proofs.

P(A) = 0.20, P(B) = 0.08, P(A n B) = 0.03

P(A) × P(B) = 0.20 × 0.08 = 0.016 ≠ 0.03

Hence, the two events aren't independent.

Further checks,

The conditional probabilities P(A|B) and P(B|A) are normally given as

P(A|B) = P(A n B) ÷ P(B)

P(A|B) = 0.03 ÷ 0.08 = 0.375 ≠ P(A) (which is 0.2)

Further proof that they are dependent events.

P(B|A) = P(A n B) ÷ P(A)

P(B|A) = 0.03 ÷ 0.20 = 0.15 ≠ P(B) (which is 0.08)

Further proof that the two events aren't independent.

Hope this Helps!!!

jainveenamrata jainveenamrata · Answer 2 · 2022-06-07T07:50:20+02:00

The rain and bus running late are dependent events.

What are independent and dependent variables?

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on the other.

If a variable is taking its values independently of any visible direct cause, then that variable is called an independent variable.

The variables that take their values based on some other variables' values are called dependent variables.

Let event A be the event that it rains. Then the probability will be

P(A) = 0.20

Let event B be the event that the bus is late. Then the probability will be

P(B) = 0.08

Let the event that it rains and the bus is late A and B, that is, (A n B). Then the probability will be

P(A n B) = 0.03

We know that

P(A n B) = P(A) x P(B)

Then we have

P(A n B) = 0.20 x 0.80

0.03 ≠ 0.16

Thus, they are not independent events.

More about the probability link is given below.

https://brainly.com/question/795909

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