Question

An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A

Answer 1

Answer:

$P(x\geq 1) = 0.923$

Step-by-step explanation:

From the question we are told that:

Percentage of student to get A $P(A)=\%5=0.05$

Sample size $n=50$

Generally Number of student to get A is

$N_a=n*P(A)$

$N_a=50*0.05$

$N_a=2.5$

Therefore

Probability that one student gets an A grade is mathematically by

  $^nPC_xP^x(1-P)^{n-x}$

 $P(x\geq 1)=1-P(x$

 $P(x\geq 1) =1-P(x=0)$

 $P(x\geq 1) =^50C_0(0.05)^0(0.95)^50$

 $P(x\geq 1) = 0.923$