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

Didi Yuli Setiaji
3 May 202117:42

Summary

TLDRThis 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.

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