Video: Using 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? [A] Impossible [B] Unlikely [C] Likely [D] Certain

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Video Transcript

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.

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