Probability of Chance Events Quick Check

Question

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Question
Use the table to answer the question.

The table displays the outcomes of a spinner landing on the letters K, I, N, and D when spun by Xavier.
Outcome K I N D
Frequency 120 140 105 135
A spinner is divided into 4 sections labeled as K
, I
, N
, D
. Xavier reproduced the wheel and uses a computer to simulate the outcomes of 500 spins. What is the approximate probability that the spinner will stop on a consonant on the next spin?

(1 point)
Responses

0.28
0.28

0.45
0.45

0.72
0.72

0.24
0.24

Answer 1

To find the probability that the spinner will stop on a consonant on the next spin, we first need to identify which letters are consonants. In this case, the letters K and N are consonants, while I and D are vowels (D is actually a consonant as well, but here we consider I to be the true vowel).

The frequencies given for each letter are:

• K: 120
• I: 140
• N: 105
• D: 135

First, we need to calculate the total number of spins, which is the sum of all frequencies: \[ 120 + 140 + 105 + 135 = 500 \]

Next, we find the total frequency for consonants (K, N, and D): \[ 120 (K) + 105 (N) + 135 (D) = 360 \]

Now, we can find the probability of stopping on a consonant: \[ P(\text{consonant}) = \frac{\text{Number of consonant outcomes}}{\text{Total outcomes}} = \frac{360}{500} = 0.72 \]

Therefore, the approximate probability that the spinner will stop on a consonant on the next spin is 0.72.