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A spinner has 8 equally sized sections labeled as $A, B, C, D, E, F, G, H$. In 160 spins, how many times can you expect to spin on a consonant?

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Answer :

First, note that the spinner has 8 equally sized sections labeled as
$$A, B, C, D, E, F, G, H.$$

Out of these, the vowels are $A$ and $E$. That means the letters that are consonants are
$$B, C, D, F, G, H.$$
There are 6 consonants.

Since the spinner is fair, the probability of landing on any one section is
$$\frac{1}{8}.$$
Thus, the probability of landing on a consonant in one spin is
$$\frac{6}{8} = 0.75.$$

If the spinner is spun 160 times, the expected number of times to land on a consonant is calculated by
$$\text{Expected number} = 160 \times 0.75 = 120.$$

Therefore, you can expect to land on a consonant $\boxed{120}$ times in 160 spins.

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