Cala rolls a biased dice 40 times. It comes up with a three 14 times. Calculate the relative frequency of rolling a three.

Antoni throws a normal six-sided dice 120 times. How many times would you expect him to throw a 4?

Binh throws a biased dice 200 times. The theoretical probability of it landing on a 2 is 0.6. How many times would you expect her to throw a 2?

Xavier has a biased coin which has a 30% chance of landing on Heads. He flips the coin 300 times. How many times would you expect it to land on Tails?

Yasmin has 200 daisy seeds to plant in her garden. The probability of a daisy growing is 0.8. How many daisies would you expect to grow?

Theoretical Probability and Relative Frequency 2

﻿- Hello, I'm Mr. Langton, and today we're going to look at comparing probabilities. All you're going to need is something to write with and something to write on. Try and find a quiet space where you won't be disturbed and when you're ready, we'll begin. We'll start with the try this activity. In these games you win if you draw a green cube from the bag. You can choose to draw from bag A or bag B. Which bag would you choose in each game? And what would happen if you combined both of the cubes in bag As and both the cubes in the two of bag Bs, which one would be most likely there? Pause the video and have a go. When you're ready, unpause it and we'll look at it together. You can pause in 3, 2, 1. Okay, let's have a go. So in game one and bag A, the probability of choosing green is three out of 11. And in bag B, it's one out of five. Now we need to compare those probabilities and see which one's the largest, don't we? So to do that, I'm gonna need a common denominator and I'm gonna go for 55. So 3/11, to make that equivalent, that's gonna be 15 out of 55, and I'm gonna need to times that by 11 over 11 and that's gonna give me 11/55, which means that bag A is more likely to win than bag B. Look at game two, the probability of choosing green is 4/5. And the probability of choosing green from bag B is 8 out to 15. It's a little bit easier for a common denominator here. I'm gonna go for 15 'cause I've just got to multiply each of these by three and that's gonna give me 12 out 15, which makes it really obvious that once again, bag A is the better one to choose. If we combine all of the cubes in the two bag As, then altogether, we're gonna have seven green out of 16. And in bag B, we're going to have 9 out of 20. So if we're gonna compare these, we need a common denominator of 16 and 20. That's gonna be a little bit tricky and 80 would do, wouldn't it? We could make both out of 80. So we need to multiply 16 by 5 to get 80. Seven time five is the numerator. That's 35 out of 80, and we need to multiply 20 by four. So you need to multiply that by four? That gives us 36, which actually means it altogether if you combine them, bag B will have a slightly higher probability of getting a green than bag A. For this task, we need to rank the probabilities from least likely to most likely. Starting with rolling a four on a six-sided dice. There's one where you can do that out of six. Rolling a prime number on a six-side dice, your prime numbers 2,3,5,7,2, so that's three. So that's three outta six, which is also 1/2. An odd number on a nine-sided dice. So 1, 3, 5, 7, 9, there are five ways out of nine. That's slightly bigger than a half. So at the moment, they're currently in ordered from smallest to largest or least likely to most likely. Rolling a number greater than 10 on a six side dice. Well, that's impossible. So that's zero and that will definitely be the lowest. If we've got to start at the least likely, that one there will be our first one, our least likely one. Next up, rolling less than a three on an eight-sided day. So less than a three is a one or a two. So that's gonna be 2/8 or a quarter. And rolling a factor of 12, factor of 12, 1, 2, 3, 4, 6, and 12. We're rolling on an eight-sided dice, so that's gonna be five options out of eight. So now we need to finish ranking them, don't we? Well, 1/6 is smaller than a quarter, so that will be second. Five eights and five ninths are both bigger than a half. One quarter is smaller than a half. So that will be third and that will be fourth. Now, since 1/8 is bigger than 1/9, that means that 5/8 is bigger than 5/9. So that will be fifth and that will be sixth. Okay, now it's your turn. Pause the video and access the worksheet. When you're ready, unpause it and we can go through it together. Good luck. How did you get on? Let's go through the answers now. Starting with question one. What's most likely? Flipping a coin and getting tails? There's a 50/50 chance to that. So that probability's 1/2. Or rolling a six sided-dice and getting a square number? So my square number is 1, 4, 9 is two. That's the only two ways outta six for that one. 2/6 is small than 1/2. So flipping a coin and getting tails is most likely. Second one, part B, flipping a coin and getting heads. Once again, that'll be 1/2. Rolling a six-sided dice and getting a factor of 24. Factor of 24, 1, 2, 3, 4, not five, 6 is, that's five outta 6. 5/6 is greater than 1/2, so that one's gonna be the most likely one, isn't it? On the six-side dice, you're getting a factor of 24. Third one, flipping according and getting tails, which once again, the probability for that is 1/2, or on the six sided-dice and getting an odd number? Well, there are three odd numbers on a dice outta six. 3/6 is equivalent to 1/2, so both of these options are equally likely. Question two, am I more likely to roll a square number on a 10-sided dice or multiple of three on a six-sided dice? Well, multiples of 3, 3, 6, 9, 12. There are only two ways that I can do that outta six. Square numbers, 1, 4, this is a 10-sided dice, so we've got nine these times. There are three ways of doing that out 10. Now, I'm gonna turn into decimal to compare them here. 3/10 is equivalent to 0.3. 2/6 is equivalent to 1/3, which is 0.3, recurring or 0.333333. So I'm more likely to get a multiple of three on a six-sided dice. Question three, in which bag am I most likely to select a white cube? Between the first bag 1, 2, 3, 4, 5, 6, 7, a white, that's 8, 9, 10, 11, 12. And in bag B, it's four out of six. Let's make those fractions equivalent. I can make that out of 12, that would be 8/12. So if that's 8/12, that's bigger than 7/12, so it's bag B, isn't it? How many green cubes do I need to add to bag B to make the probability of selecting a white cube 0.5? So at the moment, the probability is 4/6. So if I add another green cube, there will still be four white ones and that's now out of seven. If I add another green cube, there will still be four white ones and that's out of eight. So I need to add two green cubes to get my probability equivalent to 1/2. We'll finish off with the explorer activity. This one's quite tricky. By placing cubes into the bags, how many of these statements can you make true at the same time? Making green most likely to come from bag A, the probability you're getting green from A and C combined is less than the probability of getting green from B. We would expect 40 out of 100 draws from B to be green and that theoretical probability of green from C is 0.375. Pause the video and have a go. When you're ready, unpause it, we can go through it together. You can pause in 3, 2, 1. Okay, I'm gonna share some answers that you could have. I found that for bag A I could put four green ones and three white ones and I'll make it work. And I'm not gonna draw them because when we get to bag C, I'm gonna have slightly larger numbers and I don't wanna be drawing lots and lots and lots of cubes. In bag two, if I have two green and three whites, then everything will work. And in particular, 40 out of 100 because that cancels down to 2/5. Bag C, that probability needs to be 0.375, which we want nine green and 15 white. And that one's gonna work 'cause the property of getting a green now is 9 out of 24, which they both go into three, don't they? So that is three out of eight, which is 0.375. So if you've got any answers from this or any other activity that you've done with us that you'd like to share, ask your parent or carer if they'll put it on Twitter, tagging @OakNational and LearnwithOak. I'll see you later. Goodbye.

True or false: I am more likely to flip a coin and get "Heads" than I am to roll a six-sided dice and get a 4.

True or false: I am more likely to flip a coin and get "Tails" than I am to roll a six-sided dice and get an even number.

True or false: I am more likely to roll a 3 than a 5 on a six sided dice

True or false: I am more likely to roll an even number than a prime number on an eight sided dice.

True or false: I am more likely to roll a 4 on a six sided dice than on an 8 sided dice.

Comparing Probabilities

In this lesson, we will compare the probabilities of different events to see which is most likely.

Maths

Y9 Maths

Key Stage 3

Year 9

Comparing probabilities

Probability

Statistics and probability

THEME

UNIT

Representing probability

Complementary events

Calculating probabilities

Theoretical probability and relative frequency

Theoretical probability and relative frequency (Part 2)

Combined events and sample spaces (Part 1)

Combined events and sample spaces (Part 2)

Frequency trees

Calculating the probability of combined events

Combined Events and Tree Diagrams (Part 1)

Combined events and tree diagrams (Part 2)

There are 18 marbles in a bag. 13 of them are not green. What is the probability of selecting a green marble?

There are 100 cars in a car park. 40 of them are yellow. What is the probability of choosing a car that is not yellow?

In a group of ten people, the probability that at least two were born on the same day of the week is 1.

What is the probability that this fair spinner lands on an odd number?

What is the probability that this fair spinner lands on a white triangle?

I roll a dice 50 times and it lands on a "six" 38 times. What is the relative frequency of getting a "six"?

I roll a fair six-sided dice. What is the probability I roll a 4 or a 6?

Lesson overview:Comparing probabilities

Core Content

Probability: