5-D Process: Mathematical Problem Solving

Two events A and B are independent. The probability of event A occurring is 3/5, and the probability of event B occurring is 1/2. What is the probability of both events A and B occurring?

• 0.3

• 0.5

• 0.1

• 0.6

Two events A and B are such that P(A) = 1/2 and P(B) = 3/10. If the events are independent, find P(A and B).

• 0.15

• 0.20

• 0.25

• 0.30

In a bag, there are 3 red balls and 5 blue balls. Two balls are drawn one after the other without replacement. What is the probability that both balls drawn are red?

Let A be the event that the first ball drawn is red, and B be the event that the second ball drawn is red.

• P(A) = 3/8

• P(B after A) = 2/7

Using these probabilities, determine the probability that both balls drawn are red.

• 3/28

• 1/7

• 3/14

• 1/4

Consider two independent events A and B. The probability of event A occurring is 0.6, and the probability of event B occurring is 0.5. What is the probability that both events A and B occur?

• 0.1

• 0.3

• 0.5

• 0.8

Consider a square with side length 's'. If one side of the square is increased by 12 feet and the adjacent side is decreased by 3 feet, a rectangle is formed. The perimeter of this rectangle is 62 feet. Determine the original side length 's' of the square.

• 10 feet

• 11 feet

• 12 feet

• 13 feet

How can we represent the possible outcomes in a situation?

• By using a checklist

• By guessing randomly

• By ignoring the situation

• By using a probability tree, systematic list or a table

Problem: The base of a rectangle is 13 centimeters longer than the height. If the perimeter is 58 centimeters, Usr the 5-D Process to find the base and the height of the rectangle.

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A rectangular garden has a length that is 5 meters more than its width. If the perimeter of the garden is 50 meters, what are the dimensions of the garden?

• Length: 12 meters, Width: 13 meters

• Length: 18 meters, Width: 7 meters

• Length: 20 meters, Width: 5 meters

• Length: 15 meters, Width: 10 meters

A box contains red, blue, and green marbles. The number of red marbles is twice the number of blue marbles, and the number of green marbles is three more than the number of red marbles. If there are 35 marbles in total, how many blue marbles are there?

• 5 blue marbles

• 6 blue marbles

• 7 blue marbles

• 8 blue marbles

A class has 30 students. 40% of the students are boys. How many boys are there in the class?

• 18 boys

• 15 boys

• 12 boys

• 10 boys