We are given that a joint debating session is conducted between a junior class and a senior class. We are to determine the probability that a speaker selected at random will be a female from the junior class.

Statement 1: 1/5 of the total students are from the Junior class.
This implies 4/5 of the total students are from the Senior class.

Statement 1 is not sufficient. This is because we need an information on the total number of females who are juniors. An information that merely states the proportion of the total students who are juniors is not enough to compute a unique probability for selecting a female from the junior class as the speaker.

Statement 2: 1/4 of the total students are female. Implying this is the probability of male students=3/4.
This is still not sufficient to determine the probability of selecting a female from the Junior class. An additional information about the probability selecting a student from the junior class is needed in order to compute the probability of selecting a female from the junior class as the speaker.

1+2
Probability of Selecting a junior = 1/5
Probability of Selecting a Female student =1/4
P(Jf) = 1/5 * 1/4 = 1/20.

Hence combining both statements is sufficient.

The answer is C in my view

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Imo. E

A joint debating session is conducted between a certain junior class and certain senior class. What is the probability that the speaker selected at random from this group of students will be female junior?

(1) One fifth of the students are from junior class - 20% of total (group) are from junior class and 80 % of total are from senior class. Insufficient, no information about female students.
(2) One fourth of the students are female students - 25% of total (group) are female students and 75 % of total are male students. Insufficient, no information about junior class students.
1 + 2,
We can't get the accurate information about female junior class students from the given information. So, insufficient.

A joint debating session is conducted between a certain junior class and certain senior class. What is the probability that the speaker selected at random from this group of students will be female junior?

Probability of selecting a female junior = \(\frac{Number of female juniors}{Total number of students}\)

(1) One fifth of the students are from junior class
Clearly, since a ratio is given and nothing about total number of students or about number of female juniors, the option is insufficient. Had the ratio of junior female and junior male been given then it would have made sense.

INSUFFICIENT.

(2) One fourth of the students are female students
Again only a ratio of male to female is given. No breakup for ratio of junior-senior is given.

INSUFFICIENT.

Together 1 and 2
Let total number of students = 100
Then as per statement 1 Junior students = 20 and senior students = 80
As per statement 2 female students = 25 and male students = 75

From above a lot of sets of number of Junior male, Junior female, Senior male, Senior female can be worked upon. For example - 10,10,75,15 so probability = 10/100 or 15,5,60,20 so probability = 5/100
Since number of Junior female vary, probability varies.

INSUFFICIENT.

Answer E.
_________________

need to determine P of getting a speaker is female junior
#1
One fifth of the students are from junior class
total students is not know and total girls also not know insufficient
#2
One fourth of the students are female students
total students not know insufficient
from 1 & 2
jr+sr=x
Jr=x/5
Sr=4x/5
Female = x/4
so Jr Female = 5/4 value of x is not know
IMO E



A joint debating session is conducted between a certain junior class and certain senior class. What is the probability that the speaker selected at random from this group of students will be female junior?

(1) One fifth of the students are from junior class
(2) One fourth of the students are female students

We do not even need to solve such questions, only a mental map would do
Junior and female- requires multiplication of each chance. Hence both the statements are required.
Option C
_________________

A joint debating session is conducted between a certain junior class and certain senior class. What is the probability that the speaker selected at random from this group of students will be female junior?

(1) One fifth of the students are from junior class
we know nothing about being female or male
insufficient

(2) One fourth of the students are female students
we know nothing about the number of junior or number of senior
insufficient

together still insufficient, we only know the total ratio of junior, the total ratio of senior, the total ratio of male, and the total ratio of female; but don't know the linkage between being junior and female and etc.

Therefore, E