Exploring Probability and Proportions

The video tutorial introduces the concepts of probability and proportions, focusing on theoretical probability. It covers various examples, including rolling a die, tossing a coin, drawing marbles, and selecting coins from a jar. Each example demonstrates how to calculate expected outcomes using proportions and probability. The tutorial also offers an extra credit opportunity for students to calculate the total monetary value of coins in a jar.

What is the theoretical probability of rolling a six with a fair dice?

• 1/2

• 1/4

• 1/6

• 1/3

If a dice is rolled 300 times, how many times can you expect to roll a six?

• 75

• 60

• 50

• 30

What is the first step in setting up a proportion for theoretical probability?

• Multiply the outcomes

• Divide the total number of events

• Identify the desired outcome

• Calculate the total possible outcomes

How do you calculate the expected number of times an event will occur?

• Divide the number of desired outcomes by total outcomes

• Multiply the probability by the number of trials

• Subtract the number of trials from the total outcomes

• Add the probability to the number of trials

What is the purpose of setting up proportions in probability problems?

• To decrease the number of possible outcomes

• To increase the probability of an event

• To predict theoretical outcomes

• To simplify the calculations

After tossing a coin 300 times, it landed on heads 180 times. How many times is it expected to land on heads if tossed 150 times?

• 60

• 150

• 90

• 120

Based on a previous experiment, if a coin lands on heads 30 times out of 50, how many times is it expected to land on heads if tossed 200 times?

• 90

• 100

• 120

• 150

In a bag of 25 marbles, where 15 are not orange, how many non-orange marbles are expected to be drawn in 150 draws?

• 60

• 75

• 105

• 90

If a jar contains 300 coins including 90 nickels, what is the probability of drawing a nickel in one draw?

• 1/6

• 1/5

• 1/4

• 1/3

How many nickels are expected to be drawn if 40 coins are pulled from the jar?

• 20

• 15

• 12

• 10