Question

the table shows the number of students in each grade at two different schools.

	grade 9	grade 10	grade 11	grade 12	total
school b	20	20	25	15	80
total	70	45	45	40	200

compare the probability that a randomly selected student is in grade 10 at each school. move options to the blanks to complete the sentences.

the probability a student at school a is in grade 10 is blank.

the probability a student at school b is in grade 10 is blank.

it is blank that a student at school a is in grade 10 compared to a student at school b.

options: \\(\frac{5}{24}\\), \\(\frac{1}{4}\\), \\(\frac{4}{9}\\), \\(\frac{5}{9}\\), less likely, more likely, equally likely

Explanation:

Step1: Calculate probability for School A

Probability = (Number of Grade 10 students in School A) / (Total students in School A) = \( \frac{25}{120} = \frac{5}{24} \)? Wait, no, \( 25\div120=\frac{25}{120}=\frac{5}{24} \)? Wait, 25 and 120, divide numerator and denominator by 5: \( \frac{5}{24} \)? Wait, no, 25/120 simplifies to 5/24? Wait, 25 divided by 5 is 5, 120 divided by 5 is 24. Yes. Wait, but let's check School B: Number of Grade 10 students in School B is 20, total students in School B is 80. So probability is \( \frac{20}{80}=\frac{1}{4} \). Now compare \( \frac{5}{24} \) and \( \frac{1}{4} \). Convert \( \frac{1}{4} \) to 6/24. So \( \frac{5}{24} < \frac{6}{24} \), so School A's probability is \( \frac{5}{24} \)? Wait, no, wait School A's Grade 10 is 25, total 120. 25/120 = 5/24 ≈ 0.208. School B: 20/80 = 1/4 = 0.25. So 0.208 < 0.25, so School A is less likely? Wait, no, wait the options: Let's recheck.

Wait, School A: Grade 10 students: 25, total students: 120. So probability is \( \frac{25}{120} = \frac{5}{24} \) (divided numerator and denominator by 5). School B: Grade 10 students: 20, total students: 80. So probability is \( \frac{20}{80} = \frac{1}{4} \). Now, \( \frac{5}{24} \) vs \( \frac{1}{4} \). Convert \( \frac{1}{4} \) to \( \frac{6}{24} \). So \( \frac{5}{24} < \frac{6}{24} \), so the probability for School A is \( \frac{5}{24} \), School B is \( \frac{1}{4} \), and it is less likely for School A? Wait, no, wait the question says "It is ____ that a student at School A is in grade 10 compared to School B". So if School A's probability is lower, then it's less likely. Wait, but let's check the options again.

Wait, maybe I made a mistake. Let's recalculate:

School A: Grade 10: 25, Total: 120. So 25/120 = 5/24 ≈ 0.2083.

School B: Grade 10: 20, Total: 80. 20/80 = 1/4 = 0.25.

So 0.2083 < 0.25, so School A's probability is lower, so it is less likely? Wait, but the options have "less likely", "more likely", "equally likely". So:

First blank (School A): \( \frac{5}{24} \)

Second blank (School B): \( \frac{1}{4} \)

Third blank: less likely? Wait, no, wait 5/24 is approximately 0.208, 1/4 is 0.25. So 0.208 < 0.25, so School A is less likely than School B. So:

The probability a student at School A is in grade 10 is \( \frac{5}{24} \).

The probability a student at School B is in grade 10 is \( \frac{1}{4} \).

It is less likely that a student at School A is in grade 10 compared to a student at School B.

Wait, but let's check the options again. The options for the first two blanks are \( \frac{5}{24} \), \( \frac{1}{4} \), \( \frac{4}{9} \), \( \frac{5}{9} \). The third blank options are "less likely", "more likely", "equally likely".

So:

First blank: \( \frac{5}{24} \) (since 25/120 = 5/24)

Second blank: \( \frac{1}{4} \) (since 20/80 = 1/4)

Third blank: less likely (because 5/24 ≈ 0.208 < 1/4 = 0.25)

Answer:

The probability a student at School A is in grade 10 is \(\boldsymbol{\frac{5}{24}}\).
The probability a student at School B is in grade 10 is \(\boldsymbol{\frac{1}{4}}\).
It is \(\boldsymbol{less\ likely}\) that a student at School A is in grade 10 compared to a student at School B.