Can you complete the example on additive rule with the drawing of a red or an A card?

Also, can two events be mutually exclusive and independent at the same time? Why or why not? Based on the below answered part.

ANSWER: The two essential rules of Probability are the Multiplication rule and the addition rule. These rules let us decide whether an event is independent or dependent and are they mutually exclusive or not.

The Addition rule of Probability is a rule for finding the union of two events, either mutually exclusive or non-mutually exclusive.

The Addition ruleforprobabilitiesdescribes two formulas, one for theprobabilityfor either of two mutually exclusive events happening and the other for theprobabilityof two non-mutually exclusive events happening. The first formula is just the sum of theprobabilitiesof the two events.

The probability of twomutually exclusiveevents is denoted by:

P(YorZ)=P(Y)+P(Z)

Mathematically, the probability of two non-mutually exclusive events is denoted by:

P(YorZ)=P(Y)+P(Z)P(YandZ)

I found a very interesting example that many of us would be able to relate to:

Suppose that we draw a card from a well-shuffled standard deck of cards.

In a deck of cards, there are 52 cards and we needed to determine the probability of drawing a red card or an ace. In this case, the two events are not mutually exclusive. The ace of hearts and the ace of diamonds are elements of the set of red cards and the set of aces. Hence, there would be more than one probability.

• The probability of drawing a red card is 26/52
• The probability of drawing an ace is 4/52
• The probability of drawing a red card and an ace is 2/52

The Multiplication rule helps us find the probability of two events happening at the same time.

Formula: P (A and B) = P (A)* P (B|A)

The formula directs us to multiply the potential or expected outcomes of two events. In any which way, we would need to look into the likelihood of similar events from the past. Hence, this rule of the application shows that both these events are dependent on each other.

A very common example, if you rolled a die and flipped a coin the probability of getting any number on the face of the die doesn't impact whether I get head or tail on a coin.

However, whenMultiplication Rule is used in Independent events we are looking at theprobability of two events both taking place at the same time.

A very generic example that we would come across is aboutrolling a dice and then flipping a coin, these are two independent events. The probability of rolling a 1 isand the probability of a head is . (Taylor, 2017).

On the other hand, when the Addition Rule is used in two independent events, A and B, are non-mutually exclusive. The probability that A or B will occur is the sum of the probability of each event, minus the probability of the overlap.

Here is an example that was used multiple times but for obvious reasons it works- So according to the statistics "On New Year's Eve, the probability of a person having a car accident is 0.09. The probability of a person driving while intoxicated are 0.32 and the probability of a person having a car accident while intoxicated is 0.15.