Question

theoretical probability - write the probability as a fraction in lowest terms.

1. if you roll a regular 6 - faced die 1200 times, how many times (in theory) would you expect to get a 5?

think: ( p(5)=? )

Explanation:

Step1: Calculate the probability of rolling a 5

A regular 6 - faced die has 6 possible outcomes (\(1,2,3,4,5,6\)). The probability of getting a 5, \(P(5)\), is the number of favorable outcomes (1, since there is only one face with a 5) divided by the total number of outcomes. So \(P(5)=\frac{1}{6}\).

Step2: Use the formula for expected value

The formula for the expected value \(E\) of an event is \(E = n\times P\), where \(n\) is the number of trials and \(P\) is the probability of the event. Here, \(n = 1200\) and \(P=\frac{1}{6}\). Then \(E=1200\times\frac{1}{6}\).

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Answer:

You would expect to get a 5 \(200\) times.