Question Video: Calculating the Theoretical Probability of an Event | Nagwa Question Video: Calculating the Theoretical Probability of an Event | Nagwa

# Question Video: Calculating the Theoretical Probability of an Event Mathematics • Second Year of Preparatory School

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A box contains 7 white balls, 3 black balls, and 8 red balls. What is the probability that a ball drawn at random is black?

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### Video Transcript

A box contains seven white balls, three black balls, and eight red balls. What is the probability that a ball drawn at random is black?

We’re told that the ball is drawn at random, which means every ball has an equal chance of being chosen. When all outcomes in an experiment are equally likely, we can calculate the probability of a particular event occurring by dividing the number of successful outcomes by the total number of outcomes. In this case, in which we want to calculate the probability that the ball drawn is black, the successful outcomes are all the black balls in the box. The total number of outcomes is the total number of balls in the box.

The number of black balls is given in the question; it’s three. The total number of balls in the box is the sum of the number of balls of each color: seven plus three plus eight, which is 18. So, the probability that the ball drawn is black is three out of 18. We can simplify this fraction by dividing both the numerator and denominator by three. And so we find that the probability that the selected ball is black is one-sixth.

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