Lesson Video: Probability - Certain, Likely, Unlikely, Impossible Mathematics

In this video, we will learn how to describe probability using words like “certain,” “likely,” “equally likely,” “even chance,” “unlikely,” and “impossible.”

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Video Transcript

In this video, we will learn how to describe probability using words like certain, likely, even chance, unlikely, and impossible. We will begin by recalling what we mean by probability and defining some of those keywords.

Probability is the chance that something will happen. It is how likely an event will occur. We often measure probability with a number, either a fraction, a decimal, or a percentage. We can also use words, such as impossible, unlikely, even chance, likely, and certain. It is this type of measure of probability that we will focus on in this video.

As a number, probability ranges from zero, or impossible, to one or 100 percent, which is certain. This can be shown on a number or probability line. As already mentioned, if it is impossible for an event to occur, the probability equals zero. And if it is certain for an event to occur, the probability is equal to one. In the middle of these, we have a half, 0.5, or 50 percent. At this point, we say there is a 50-50 or even chance of the event occurring. An example of this is tossing a coin as there is an equal or even chance of landing on heads or tails.

If there is less than an even chance of an event occurring, we say it is unlikely to happen. In a similar way, if the chance of an event happening is greater than an even chance, we say it is likely to happen. It is these five words that we will use to answer the questions in this video.

If this spinner is spun, which of the following describe the probability that the spinner lands on blue? Is it (A) impossible, (B) unlikely, (C) equally likely for it to happen or not happen, (D) likely, or (E) certain?

We know that the probability is the chance of an event happening, and our probability scale goes from zero to one. If an event is impossible, it cannot happen. And if an event is certain, it must happen. In the middle of this, we have an even or equal chance. This means that it is equally likely for an event to happen or not happen. If the chance of an event happening is less than this, we say it is unlikely. And if the probability or chance is greater than this, we say it is likely.

In this question, we are interested in the probability or chance that the spinner lands on blue. We can see from the figure that five out of the 10 sections of the spinner are blue. Five-tenths is equal to one-half. As this is also equal to 50 percent, there is a 50-50 chance that the spinner lands on blue. We can, therefore, conclude that option (C) is correct. It is equally likely for the spinner to land on blue or not land on blue. This is because five sections or half the spinner is blue and five sections or half the spinner are not blue.

Our next question will involve a bag containing marbles.

A bag contains 35 marbles, 34 of which are blue. If a marble is picked out at random, what is the likelihood of it being blue?

We can begin this question by recalling our probability scale. This goes from zero to one. If an event is impossible, it has a probability of zero. And if an event is certain, it has a probability of one. In the middle of these, we have a 50-50 or even chance. This is when it is equally likely that an event happens or does not happen. If the chance of an event happening is less than this, we say it is unlikely. And if the chance of an event happening is greater than this, we say it is likely.

In this question, there are 35 marbles in the bag. 34 of them are blue. This means that the probability of selecting a blue marble at random is 34 out of 35 or thirty-four thirty-fifths. This is significantly greater than an even or 50-50 chance. However, it is not certain as one of the marbles is not blue. In order for the probability to be certain, all of the marbles in the bag would have to be blue. We can, therefore, conclude that it is likely that the marble selected is blue.

We could actually go into a bit more detail here and say that it is very likely that the marble is blue. This is because 34 out of 35 is very close to one. The closer to one the probability is, the more likely the event is to happen. For the purposes of this question though, the correct answer is likely.

Our next question is another one involving a spinner.

If the spinner is spun once, determine whether it is certain, likely, unlikely, or impossible that the pointer stops on a number that is a multiple of three.

Let’s begin by recalling what we mean by a multiple of a number. The multiples of any number are the multiples in that times table. This means that the multiples of three are three, six, nine, 12, 15, and so on. We can see that eight, 10, 19, 11, and 23 are not multiples of three as these numbers are not in the three times table. 24, on the other hand, is a multiple of three. This means that one out of the six numbers on the spinner is a multiple of three. The probability can, therefore, be written as one out of six or one-sixth.

We are asked to decide whether this corresponds to the event being certain, likely, unlikely, or impossible. We know that when the probability is equal to zero, the event is impossible. And when it is equal to one, the event is certain to happen. When an event is equally likely to happen or not happen, we say there is an even chance. This is when the probability is equal to one-half. If the probability is less than this, we say the event is unlikely to happen. And if it is greater than one-half, we say it is likely to happen.

As we can see from the diagram, one-sixth is less than one-half. This means that it is unlikely that the pointer stops on a number that is a multiple of three.

In our next question, we can also use a probability scale to describe the probability of an event.

There are 15 letter tiles in a bag. Six tiles are labeled S, eight tiles are labeled R, and one is labeled M. Which of the following describes how likely it is to choose the letter M? Is it (A) impossible, (B) unlikely, (C) likely, or (D) certain?

We recall that our probability line or scale goes from zero to one. If the probability is equal to zero, it is impossible for it to happen. And if the probability is equal to one, it is certain the event will happen. In the middle of these, we have a 50-50 or even chance. Anything less than this is said to be unlikely, and anything greater than this is likely.

In this question, we are interested in the probability of selecting the letter M. As only one of the 15 letter tiles is labeled M, the probability of selecting the letter M is one out of 15. This can be written as a fraction as one over 15 or one fifteenth. One fifteenth is less than a half, but it is greater than zero. This means that the probability of selecting the letter M lies between impossible and even chance. We can, therefore, conclude that the correct answer is option (B) unlikely.

We could actually say that the probability is very unlikely as it is much closer to zero than one-half. Whilst we are not asked about the letter S and letter R in this question, the probability of selecting letter S would be six out of 15 and the probability of selecting letter R would be eight out of 15. These could also be placed on the probability line as shown. As six out of 15 is also less than a half, the probability of selecting the letter S would also be unlikely. Eight out of 15 is greater than a half, so there would be more than an even chance of selecting the letter R. We can, therefore, conclude that the chance of selecting a letter R would be likely.

In our final question, we will look at another problem involving a spinner.

Is it more likely, equally likely, or less likely that this spinner lands on red rather than green?

We can see on the diagram that our spinner has been split into 10 equal sections. Of these, four are blue. Two of the sections are yellow. Two of the sections are green. Finally, two of the sections are red. In this question, we are interested in the sections that are red and green.

We have already seen that two out of the 10 sections are green and two out of the 10 sections are red. As the same number of sections are red and green, we can say that it is equally likely that the spinner lands on red and green.

Whilst we’re not asked to in this question, we could write these probabilities as fractions. There is a two-out-of-10 or two-tenths chance of landing on green or red. This could be simplified to one-fifth or one out of five. There is a one-in-five chance that the spinner lands on red and a one-in-five chance that it lands on green.

This is also true of yellow as there are two yellow sections on the spinner. The probability of landing on blue, however, would be four-tenths, which simplifies to two-fifths, as four out of the 10 sections are blue.

We will now conclude this video by summarizing the key points. The probability of an event occurring is how likely it is to happen, and it ranges from zero to one. We know that when the probability is equal to zero, it is impossible for the event to happen. If an event is certain to happen, the probability is equal to one. If it is equally likely that an event happens or does not happen, we say there is a 50-50 or even chance. If the probability is less than this, we say it is unlikely to happen. And if it is greater than this, it is likely to happen.

We saw in this video that we can use these five keywords to describe the probability of an event occurring. This can include spinning a spinner or selecting marbles or balls from a bag.

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