Explain what you've used and why?
There are a large number of students in Luttley College. 60% of the students are boys. Students can
choose exactly one of Games, Drama or Music on Friday afternoons. It is found that 75% of the boys
choose Games, 10% of the boys choose Drama and the remainder of the boys choose Music. Of the
girls, 30% choose Games, 55% choose Drama and the remainder choose Music.
5 Drama students are chosen at random. Find the probability that at least 1 of them is a boy.
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asked by Raj
today at 8:45am
say s students
Boys = .6 s
.75 (.6) s = games
.1 (.6) s = drama
.15 (.6) s = music
Girls = .4 s
.3 (.4) s = games
.55(.4) s = drama
.15(.4) s = music
so number of drama students = .06 s + .22 s = .28 s
so if you pick one dram student
p one boy drama student in one pick = .06/.28 = .214
now do your Bernoulli thing for 1 of 5
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Damon
today at 9:04am
Oh, easier find the probability that all are girls then subtract from one :)
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Damon
today at 9:22am
How to know where to use conditional probability as in this question?
To know where to use conditional probability in a question like this, you need to carefully analyze the given information and identify the variables involved. In this specific question, the variables are the gender of the students (boys or girls) and the choice of activity (Games, Drama, or Music).
The conditional probability comes into play when you need to calculate the probability of an event given that another event has already occurred. In this case, you are asked to find the probability that at least 1 of the 5 randomly chosen drama students is a boy.
To solve this, you can use the concept of complementary probability. First, find the probability that all 5 chosen students are girls. Then, subtract this probability from 1 to find the probability that at least 1 of them is a boy.
In this question, you can calculate the probability of choosing a girl drama student using the information given: 55% of girls choose Drama and the total number of girls is 40% of the total number of students. Multiply these two probabilities together to find the probability that a student is a girl drama student.
Next, raise this probability to the power of 5 because you need to find the probability that all 5 chosen students are girl drama students.
Finally, subtract this probability from 1 to find the probability that at least 1 of the 5 chosen students is a boy.
In summary, you use conditional probability in this question by calculating the probability of an event (all chosen students are girls) given that another event (chosen students are drama students) has already occurred.