Question

On a December day, the probability of snow is 0.30. The probability of a "cold" day is 0.50. The probability of snow and "cold" weather is 0.15. Are snow and "cold" weather independent events?a only if given that it snowedb Noc Yesd only when they are also mutually exclusive

Answer 1

Answer:

Yes, snow and cold weather are independent.

Step-by-step explanation:

We are given the following in the question:

C: Cold weather

S: Snow

P(C) = 0.50

P(S) =0.30

$P(S\cap C) = 0.15$

We have to check whether snow and cold whether are independent events.

If the events A and B are independent then,

$p(A\cap B) = P(A)\times P(B)$

Checking,

$p(S\cap C) = P(S)\times P(C)\\0.15 = 0.30\times 0.50$

Thus, the two events are independent.

For mutually exclusive events

$P(A\cap B) = 0$

Thus, the given events are not mutually exclusive.

Answer 2

Considering that $P(A \cap B) = P(A)P(B)$, it is found that they are independent, hence option c is correct.

Two events, A and B, are independent if:

$P(A \cap B) = P(A)P(B)$

In this problem, the events are:

• Event A: Snow.

• Event B: Cold.

The probabilities are:

• On a December day, the probability of snow is 0.30, hence $P(A) = 0.3$.

• The probability of a "cold" day is 0.50, hence $P(B) = 0.5$.

• The probability of snow and "cold" weather is 0.15, hence $P(A \cap B) = 0.15$

The multiplication is:

$P(A)P(B) = 0.3(0.5) = 0.15$.

Since $P(A \cap B) = P(A)P(B)$, it is found that they are independent, hence option c is correct.

You can learn more about independent events at https://brainly.com/question/14478923