School a has so many students in it that it is divided into 15 classes.  School a students are known as outstanding students and has an extraordinary memory.  From the number of students, a sample is taken for a research as many as 30 students. From 30 students, 10 students are known from the sample have a memory of more than 10,000 sentences. What is the probability that 3 out of 8 students have a memory of more than 10,000 sentences?

The required probability is:

P = 0.3179

Step-by-step explanation

Let x be a hypergeometric variable representing no of students in population who have memory of more than 10,000 sentences. The corresponding hypergeometric probability is:

P(X=x)=NCn?kCx?×N−kCn−x??

Here we have:

k= No of successes in population( No of students having more than 10,000 sentences memory in population) = 10

N= Population size= 30

n= Sample size=8

x= no of successes in sample(No of students having more than 10,000 sentences memory in sample) = 3

The corresponding probability that 3 out of 8 students have memory of more than 10,000 words is:

P(X=3)=30C8?10C3?×30−10C8−3??

P(X=3)=0.3179