Akoy nagbuhat ani ayaw pataka nga kinuha nako

3. FIND THE PROBABILITY
OF (A ⋃ B)
Find the percentage or rate or percent in a given problem

4. UNION – Two events are mutually exclusive events when they cannot
occur at the same time
INTERSECTION - if they will occur at the same time, then they are not
mutually exclusive
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
1. P(A) is the probability of drawing a red card, which is
6
10
or 0.6.
2.P(B) is the probability of drawing a blue card, which is
4
10
or
0.4.
3.P(A ∩ B) is the probability of drawing both red and blur
card at the same time. Since a card cannot be both red and
blue, this probability is 0.

5. Now, let’s use the formula to find the probability of A U B:
P(A U B) = P(A) + P(B) – P(A ∩ B)
P(A U B) =0.6 + 0.4 – 0
P(A U B) =1
So, the probability of either drawing a red card or blue card or both is 1 or
100%. This means if you draw a card from the deck, you’re guaranteed to
get either a red card or blue card.

6. Event A: Tossing a fair six- sided die and getting an even number.
Event B: drawing a card from a standard deck of playing cards and getting a heart
1. Probability of Event A (getting an even number when tossing a die): Out of six
possible outcomes (1,2,3,4,5,5), three are even numbers (2,4,6). So the
probability of getting an even number is
3
6
=
1
2
.
2. Probability of Event B (drawing a heart attack from a deck of cards): In a
standard deck of 52 cards there are 13 hearts. So, the probability of drawing a
heart is
13
52
=
1
4
Now, let’s find the probability of A ∪ B, which means getting either an even
number when tossing a die or drawing a heart ( or both).
To find A ∪ B, we add the probabilities of A and B, then subtract the probability of
both A and B happening at the same time to avoid double counting

7. To find A ∪ B , we add the probabilities of A and B, then subtract the probability of both A and B happening at the
same time to avoid double counting.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Now, let’s find P(A ∩ B), which is the probability of both events A and B happening simultaneously. Since getting
an even number on a die and drawing a heart from a deck of cards are independent events, we can multiply their
probabilities:
P(A ∩ B) = P(A) × P(B)
P(A ∩ B) =
1
2
×
1
4
P(A ∩ B) =
1
8
Now Let’s go back to the original formula:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A ∪ B) =
1
2
+
1
4
−
1
8
P(A ∪ B) =
5
8
So, the probability of getting either an even number when tossing a die or drawing a heart from a deck of cards
(or both) is
5
8
.

8. Example 1: Red Cards and 6s:
• Suppose we randomly select a card from a standard deck of 52 cards. We want to find the
probability of selecting either a red card or a 6.
■ Let:
(A): Probability of getting a red card.
(B): Probability of getting a 6.
■ Given:

9. Example 1: Red Cards and 6s:
• Suppose we randomly select a card from a standard deck of 52 cards. We want to find the
probability of selecting either a red card or a 6.
■ Let:
(A): Probability of getting a red card.
(B): Probability of getting a 6.
■ Given:
Number of red cards = 26
Number of 6-labeled cards = 4
Number of red cards labeled 6 = 2

10. Example 1: Red Cards and 6s:
• Suppose we randomly select a card from a standard deck of 52 cards. We want to find the
probability of selecting either a red card or a 6.
■ Let:
(A): Probability of getting a red card.
(B): Probability of getting a 6.
■ Given:
Number of red cards = 26
Number of 6-labeled cards = 4
Number of red cards labeled 6 = 2

11. ■ Calculations:
(P(A) =
26
52
(P(B) =
4
52
(P(A∩B) =
2
52
• Using the formula:
[P(AUB) = P(A) + P(B) - P(A∩B)
=
26
52
+
4
52
-
2
52
=
30
52
-
2
52
=
28
52
=
7
13
• Answer: The required probability is
7
13

12. Example 2:
Dice and Coin:
• If we roll a fair six-sided die and flip a coin simultaneously, what is the probability of getting
either a 2 on the die or tails on the coin?
■ Let:
(A): Probability of getting a 2 on the die.
(B): Probability of getting tails on the coin.
■ Since 2 and tails are mutually exclusive (we cannot get both in the same roll),
(P(A∩B) = 0).
■ Calculations: (P(A) =
1
6
(P(B) =
1
2
• Using the formula:
[P(AUB) = P(A) + P(B) P(A∩B)
=
1
6
+
1
2
- 0
=
2
6
=
1
3
■ Answer: The required probability is
1
3
Remember, the (P(AUB)) formula accounts for both
overlapping and mutually exclusive events.

13. To find the probability of (AUB), you need to use the formula:
P(AUB) = P(A) + P(B)P(AB)
This means that the probability of either A or B happening is equal to the sum of the probabilities
of A and B happening Individually, minus the probability of both A and B happening together.
To find the percentage, rate, or base in a given problem, you need to use the formula:
P = B x R
This means that the percentage (P) is equal to the base (B) times the rate. The base is the whole
amount or quantity, the rate is the fraction or proportion, and the percentage is the part or
portion.
For example, if you want to find the percentage of 12 out of 20, you can use the formula:
P = B x R
P = 20 x
12
20
P = 12

14. Suppose you bought a shirt that was originally priced at 800 pesos, but it was on sale for 20% off.
You want to find out how much you saved and how much you paid for the shirt. You can use the
formula: P=BxR Let B be the base, which is the original price of the shirt, and R be the rate, which is
the discount percentage. Then:
B = 800
R = 0.20
Plugging these values into the formula, we get:
P = 800 × 0.20
P=160
This means that the percentage (P) is 160 pesos, which is the amount you saved. To find out how
much you paid for the shirt, you can subtract the percentage from the base:
B-P800-160
B-P640
This mean that you paid 640 pesos for the shirt after the discount