the spinner shown has 8 congruent sections. the spinner is spun 96 times. what is a reasonable prediction…

the spinner shown has 8 congruent sections. the spinner is spun 96 times. what is a reasonable prediction for the number of times the spinner will land on a prime number? a 36 b 12 c 48 d 24

the spinner shown has 8 congruent sections. the spinner is spun 96 times. what is a reasonable prediction for the number of times the spinner will land on a prime number? a 36 b 12 c 48 d 24

Answer

Explanation:

Step1: Identify prime numbers

Prime numbers among (2,11,16,18,20,21,28,35) are (2) and (11). So there are (2) prime - numbered sections out of (8) total sections.

Step2: Calculate the probability

The probability (P) of landing on a prime number is (P=\frac{\text{Number of prime - numbered sections}}{\text{Total number of sections}}=\frac{2}{8}=\frac{1}{4})

Step3: Predict the number of times

If the spinner is spun (n = 96) times, the expected number of times (E) it lands on a prime number is (E=n\times P). Substitute (n = 96) and (P=\frac{1}{4}) into the formula: (E=96\times\frac{1}{4}) [ \begin{align*} E&=\frac{96}{4}\ & = 24 \end{align*} ]

Answer:

D. 24