To find the probability that a group will take a selfie exactly 5 times, we need to follow several steps:
### Step 1: Determine Total Number of Groups
First, we need to determine the total number of groups. This is done by summing up the frequencies in the given data.
[tex]\[
\text{Total number of groups} = 27 + 29 + 18 + 14 + 12
\][/tex]
Adding these values, we get:
[tex]\[
27 + 29 = 56
\][/tex]
[tex]\[
56 + 18 = 74
\][/tex]
[tex]\[
74 + 14 = 88
\][/tex]
[tex]\[
88 + 12 = 100
\][/tex]
So, the total number of groups is 100.
### Step 2: Find the Frequency of Groups Taking a Selfie Exactly 5 Times
Next, we look at the frequency of groups that took a selfie exactly 5 times. From the table, we see that:
[tex]\[
\text{Frequency of groups taking a selfie 5 times} = 12
\][/tex]
### Step 3: Calculate the Probability
To find the probability that a group will take a selfie exactly 5 times, we divide the frequency of groups taking 5 selfies by the total number of groups.
[tex]\[
P(5) = \frac{\text{Frequency of groups taking a selfie 5 times}}{\text{Total number of groups}}
\][/tex]
Substituting the numbers:
[tex]\[
P(5) = \frac{12}{100}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
P(5) = 0.12
\][/tex]
### Step 4: Express the Probability
Therefore, the probability that a group will take their selfie exactly 5 times is:
[tex]\[
P(5) = 0.12
\][/tex]
So, the probability a group will take their selfie exactly 5 times is [tex]\( 0.12 \)[/tex] or 12%.
