To determine how many times you can expect to spin a consonant in two spins of the spinner, we first identify the consonants among the labels A, B, C, D, E, F, G, and H.
The consonants are: B, C, D, F, and G. This gives us a total of 5 consonants out of 8 sections.
The probability of landing on a consonant in a single spin is:
\[ P(\text{consonant}) = \frac{\text{number of consonants}}{\text{total sections}} = \frac{5}{8} \]
When spinning the spinner twice, we want to find the expected number of spins that result in consonants. The expectation for one spin is given by \(P(\text{consonant})\), and for two spins, the expectation would be:
\[ E(\text{consonants in 2 spins}) = 2 \times P(\text{consonant}) = 2 \times \frac{5}{8} = \frac{10}{8} = 1.25 \]
Now, since we want to know how many times we can expect to get 2 consonants over 160 spins, we need to calculate how many pairs of spins are in 160 spins. Since every 2 spins constitutes one "pair," we will have:
\[ \text{number of pairs} = \frac{160}{2} = 80 \]
Thus, the expected number of times to get 2 consonants in those 80 pairs is:
\[ E(\text{2 consonants in 80 pairs}) = 80 \times E(\text{2 consonants in one pair}) = 80 \times 1.25 = 100 \]
Therefore, you can expect to spin on consonants 100 times in 160 spins.