PROBABILITY OF UNION OF TWO EVENTS || GRADE 10 MATHEMATICS Q3

Summary

This video lesson explains the concept of probability, focusing on the union of two events. It covers both mutually exclusive and non-mutually exclusive events, with clear formulas for calculating their probabilities. Examples include drawing cards from a deck, selecting balls from a bag, and determining the probability of watching two television channels. The video uses practical, real-life examples to illustrate the concepts, and it demonstrates how to calculate probabilities step-by-step. The lesson is designed to help viewers understand and apply basic probability principles in various contexts.

Takeaways

• 😀 Mutually exclusive events: When two events (A and B) cannot happen together, the probability ofVideo Script Takeaways their intersection is 0.
• 😀 For mutually exclusive events, the probability of their union is the sum of the individual probabilities: P(A or B) = P(A) + P(B).
• 😀 In a deck of cards, the probability of drawing a queen or a king is the sum of their individual probabilities: P(Queen or King) = 2/13.
• 😀 In the case of a bug with 7 white, 11 orange, and 12 red balls, the probability of drawing a white or red ball is 19/30.
• 😀 When events are mutually exclusive, the formula for calculating the probability of the union remains P(A or B) = P(A) + P(B).
• 😀 Non-mutually exclusive events: The formula for the union is adjusted by subtracting the intersection: P(A or B) = P(A) + P(B) - P(A and B).
• 😀 Example: The probability of drawing a heart or a face card in a deck is calculated as P(Heart or Face) = (13/52 + 12/52 - 3/52) = 22/52.
• 😀 The probability of drawing a number card or an ace in a deck of cards is 40/52, which simplifies to 10/13.
• 😀 For non-mutually exclusive events like drawing a spade or a jack from a deck, the formula accounts for overlap (P(Spade or JackProbability Key Takeaways) = 16/52 = 4/13).
• 😀 The concept of 'intersection' helps adjust the probability of non-mutually exclusive events by removing the overlap between the two sets of events.

Q & A

What does it mean for two events to be mutually exclusive?

Two events are mutually exclusive if they cannot happen at the same time. In other words, the probability of both events occurring together is zero.

How do you calculate the probability of the union of two mutually exclusive events?

For mutually exclusive events, the probability of the union is simply the sum of the individual probabilities. That is, P(A or B) = P(A) + P(B).

What is an example of finding the probability of drawing a queen or a king from a deck of cards?

In an ordinary deck of 52 cards, the probability of drawing a queen or a king is calculated by adding the individual probabilities. Since there are 4 queens and 4 kings, the probability is P(queen or king) = (4/52) + (4/52) = 8/52 = 2/13.

How would you find the probability of drawing a white or red ball from a box with 7 white, 11 orange, and 12 red balls?

First, calculate the total number of balls (7 + 11 + 12 = 30). Then, the probability of drawing a white ball is 7/30, and the probability of drawing a red ball is 12/30. The total probability is the sum of these two, 7/30 + 12/30 = 19/30.

What is the formula for calculating the probability of the union of two non-mutually exclusive events?

For non-mutually exclusive events, the probability of the union is calculated by P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) is the probability of both events occurring together.

In a deck of cards, what is the probability of drawing a heart or a face card?

There are 13 hearts and 12 face cards (Jack, Queen, King from all suits). Since there are 3 face cards in the hearts suit, the intersection is 3/52. The probability is P(heart or face card) = (13/52) + (12/52) - (3/52) = 22/52 = 11/26.

How would you calculate the probability of drawing a black card or a diamond card from a deck of cards?

There are 26 black cards (13 spades and 13 clubs) and 13 diamonds. Since there is no overlap between black cards and diamonds, the probability is simply the sum of these probabilities: P(black card or diamond) = (26/52) + (13/52) = 39/52 = 3/4.

How is the probability of selecting a number divisible by 3 or 4 from the first 50 positive integers calculated?

To calculate this, first find the numbers divisible by 3 (16 numbers) and those divisible by 4 (12 numbers). The intersection (numbers divisible by both 3 and 4) is the set of numbers divisible by 12, which is 4 numbers. Therefore, the probability is P(divisible by 3 or 4) = (16/50) + (12/50) - (4/50) = 24/50 = 12/25.

If 60% of residents in a city are watching either ABS-CBN or GMA, and 30% are watching ABS-CBN and 40% are watching GMA, how do you calculate the percentage of residents watching both channels?

Use the formula for non-mutually exclusive events: P(A or B) = P(A) + P(B) - P(A and B). Here, P(A or B) = 0.60, P(A) = 0.30, and P(B) = 0.40. Solving for P(A and B) gives 0.60 = 0.30 + 0.40 - P(A and B), so P(A and B) = 0.10 or 10%.

What is the significance of using the formula P(A or B) = P(A) + P(B) - P(A and B) for non-mutually exclusive events?

This formula adjusts for the overlap between events A and B, ensuring that the probability of both events occurring together is not counted twice. It's crucial when the events are not mutually exclusive, meaning they can happen together.