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Answer :
To solve the problem, we start by determining the following:
1. The spinner is divided into 8 equally sized sections.
2. The sections are labelled with the letters [tex]$\{A, B, C, D, E, F, G, H\}$[/tex]. Among these letters, the vowels are [tex]$A$[/tex] and [tex]$E$[/tex]. This means there are 2 vowels.
3. The remaining letters are consonants. Therefore, the number of consonant sections is:
[tex]$$8 - 2 = 6.$$[/tex]
4. The probability of spinning on a consonant in one spin is:
[tex]$$\frac{6}{8} = \frac{3}{4}.$$[/tex]
5. Given that the spinner is spun 160 times, the expected number of spins landing on a consonant is:
[tex]$$160 \times \frac{3}{4} = 120.$$[/tex]
Thus, you can expect to spin on a consonant [tex]$\boxed{120}$[/tex] times.
1. The spinner is divided into 8 equally sized sections.
2. The sections are labelled with the letters [tex]$\{A, B, C, D, E, F, G, H\}$[/tex]. Among these letters, the vowels are [tex]$A$[/tex] and [tex]$E$[/tex]. This means there are 2 vowels.
3. The remaining letters are consonants. Therefore, the number of consonant sections is:
[tex]$$8 - 2 = 6.$$[/tex]
4. The probability of spinning on a consonant in one spin is:
[tex]$$\frac{6}{8} = \frac{3}{4}.$$[/tex]
5. Given that the spinner is spun 160 times, the expected number of spins landing on a consonant is:
[tex]$$160 \times \frac{3}{4} = 120.$$[/tex]
Thus, you can expect to spin on a consonant [tex]$\boxed{120}$[/tex] times.
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