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Question Video: Determining the Total Number of Trials in an Experiment Mathematics

The experimental probability that a coin lands on heads is 4/7. If the coin landed on tails 30 times, how many times was it tossed in the experiment?

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Video Transcript

The experimental probability that a coin lands on heads is four-sevenths. If the coin landed on tails 30 times, how many times was it tossed in the experiment?

This question is about experimental probability. We recall that experimental probability can be written as a fraction, where the numerator is the number of trials in which the outcome occurs and the denominator is the total number of trials. We are told that the probability that the coin lands on heads is four-sevenths. Since probabilities sum to one, the probability of the coin landing on tails is one minus four-sevenths, which is equal to three-sevenths.

We are also told that the coin landed on tails 30 times. If we let the total number of trials be 𝑛, then we have three over seven is equal to 30 over 𝑛. To solve for 𝑛, we begin by cross multiplying. As seven multiplied by 30 is 210, we have three 𝑛 is equal to 210. Dividing through by three, we have 𝑛 is equal to 70. We can therefore conclude that the coin was tossed 70 times in the experiment.

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