Peluang Kejadian Majemuk (Peluang Saling Lepas dan Tidak Saling Lepas)

Summary

This video explains the concepts of **mutually exclusive events** and **non-mutually exclusive events** in probability theory. The presenter discusses the formulae for calculating the probability of each event type, providing examples like rolling dice and drawing cards from a deck. For mutually exclusive events, the probability is the sum of the individual probabilities, while for non-mutually exclusive events, the intersection is subtracted to avoid double-counting. The explanation includes practical examples such as rolling a die for odd or even numbers and drawing specific cards from a deck, making it an accessible and informative guide to basic probability principles.

Takeaways

• 😀 Disjoint events are events that cannot occur at the same time, such as rolling an odd or even number on a die.
• 😀 For disjoint events, the probability of either event occurring is the sum of the individual probabilities.
• 😀 Example 1: When rolling a die, the probability of rolling an odd or even number is 1 (or 100%).
• 😀 Disjoint events are also known as mutually exclusive events, meaning they have no overlap.
• 😀 In non-disjoint events, the two events can occur at the same time, such as rolling a prime number or an even number on a die.
• 😀 For non-disjoint events, the probability of either event occurring is the sum of their individual probabilities minus the probability of both events happening simultaneously.
• 😀 Example 1: When rolling a die, the probability of rolling a prime or even number is 5/6, accounting for the overlap of number 2.
• 😀 When dealing with non-disjoint events, it's crucial to subtract the overlap from the combined probabilities to avoid double-counting.
• 😀 Non-disjoint events can occur in various situations, like drawing a king or a black card from a deck of cards.
• 😀 Example 2: When drawing a card from a deck, the probability of drawing a king or a black card is 28/52 after accounting for overlap (king of spades and king of clubs).

Q & A

What is the difference between mutually exclusive and non-mutually exclusive events?

Mutually exclusive events cannot happen at the same time, meaning if one event occurs, the other cannot. Non-mutually exclusive events can happen simultaneously, meaning there is an overlap between the two events.

How do you calculate the probability of mutually exclusive events?

For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This is calculated using the formula: P(A or B) = P(A) + P(B).

Can you provide an example of mutually exclusive events?

Yes. If you roll a die and want the probability of either an odd or even number showing up, these events are mutually exclusive because a die cannot show both an odd and an even number at the same time.

What formula is used to calculate the probability of non-mutually exclusive events?

For non-mutually exclusive events, the formula is: P(A or B) = P(A) + P(B) - P(A and B). This formula accounts for the overlap between events A and B, ensuring that the shared outcomes are not counted twice.

How does the probability of rolling an odd or even number on a die demonstrate mutually exclusive events?

When rolling a die, the events of rolling an odd or even number are mutually exclusive because a single roll can only result in one outcome—either an odd number or an even number, but not both at the same time.

What is the probability of rolling an odd or even number on a die?

There are 3 odd numbers (1, 3, 5) and 3 even numbers (2, 4, 6) on a die. The probability of rolling either an odd or even number is P(odd or even) = 3/6 + 3/6 = 6/6 = 1.

What is the probability of rolling a sum of 4 or 11 with two dice?

The probability of rolling a sum of 4 or 11 with two dice is calculated by adding the individual probabilities of getting a sum of 4 or 11. There are 3 ways to roll a sum of 4 and 2 ways to roll a sum of 11. So, P(4 or 11) = 5/36.

How do you determine if two events are mutually exclusive when using cards?

Two events with cards are mutually exclusive if they cannot both occur at the same time. For example, drawing a red card or a black card from a deck is mutually exclusive because a card can only be either red or black, not both.

What does the term 'overlap' mean in the context of non-mutually exclusive events?

Overlap refers to the common outcomes that are shared between two events. In non-mutually exclusive events, there are outcomes that belong to both events, and these must be subtracted to avoid double-counting them.

How do you calculate the probability of drawing a King or a black card from a deck of cards?

To calculate the probability of drawing a King or a black card, you add the probability of drawing a King and the probability of drawing a black card, then subtract the probability of drawing the King of Spades (which is counted in both categories). The formula is P(King or black) = P(King) + P(black) - P(King of Spades), resulting in 28/52, which simplifies to 7/13.