Video: Determining the Union of Two Mutually Exclusive Events

A bag contains fifty-one balls numbered 1 to 51. If one ball is randomly drawn from the bag without looking, what is the probability that it is numbered 17 or 27? Give your answer as a fraction in its simplest form.

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Video Transcript

A bag contains 51 balls numbered one to 51. If one ball is randomly drawn from the bag without looking, what is the probability that it is numbered 17 or 27? Give your answer as a fraction in its simplest form.

In order to write probability as a fraction, we need to work out the number of successful outcomes and the number of possible outcomes. In this case, there are 51 balls in total. Therefore, there are 51 possible outcomes. This means that our denominator, or bottom number, of our fraction is 51.

As we want to calculate the probability that the ball selected is either 17 or 27, there are two successful outcomes. This means that the numerator is two. Therefore, the probability of selecting 17 or 27 from a bag of 51 balls numbered one to 51 is two out of 51. The question asked for a fraction in its simplest form. As the only common factor of two and 51 is one, the fraction is already in its simplest form, two out of 51.

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