In the previous examples, we were always involved in finding the probability of a single event. For example:
- The probability of getting an ace card from a deck of 52 cards.
- The probability of selecting three bowlers from a list of four, and so on.
Now, what about two events occurring simultaneously? For example, what would be the probability of selecting an ace card or a heart card from the deck? How would this specific probability relate to the individual probabilities, i.e., the probability of getting a heart card separately and the probability of getting an ace card separately? This is something that you will get to learn using the two important rules related to probability – addition and multiplication. First, we will discuss the addition rule in the upcoming video.
Note
At 3:07 the SME says the probability of heart card is 13/12 but the correct value is 13/52 (as shown in the PPT).
So, to summarise the learnings from the video, when you have the individual probabilities of two events A and B, denoted by P(A) and P(B), the addition rule states that the probability of the event that either A or B will occur is given by:
P(A∪B) = P(A) + P(B) – P(A∩B),
where, P(A∪B) denotes the probability that either event A or B occurs.
P(A) denotes the probability that only event A occurs
P(B) denotes the probability that only event B occurs
P(A∩B) denotes the probability that both events A and B occur simultaneously.
Note
The symbols ∪ and ∩ are obtained from the world of ‘set theory‘ and are used to denote union and intersection, respectively. You do not need to learn about them in detail right now. All you need to learn are the meanings of the probability terms mentioned earlier. Also, we would be skipping the proof of the formula right now. Another important thing to note here is that the formula mentioned earlier works for all types of events A and B, irrespective of the fact that they are independent or disjoint.
You can also read P(A∪B) as P(either event A or B occurs) and P(A∩B) as P(both events A and B occur).
As mentioned in the video, for disjoint events A and B, P(A∩B) = 0 since both cannot occur simultaneously. Hence, the formula can be rewritten as P(A∪B) = P(A) + P(B).
Now, answer the following questions.
In the next segment you will learn about the multiplication rule of probability.