We need to spin the spinner <u>150 times</u>, to expect a multiple of 4 to be spun 30 times.
In the question, we are given that a spinner is divided into 15 identical sectors and labeled 1 through 15.
We are asked the number of times the spinner must be spun to expect a multiple of 4 30 times.
The possible outcomes of a multiple of 4 are 4, 8, and 12.
Thus, the number of possible outcomes are 3.
The total number of outcomes are 15.
Thus, the probability of getting a multiple of 4 in one spin = 3/15 = 1/5.
Thus, to expect a multiple of 4 once, we need to spin the spinner 5 times.
Thus, to expect a multiple of 4 30 times, we need to spin the spinner 5 * 30 = 150 times.
Thus, we need to spin the spinner <u>150 times</u>, to expect a multiple of 4 to be spun 30 times.
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