Question

If the overall percentage of success in an exam is 60, what is the probability that out of a
group of 4 students, at least one has passed?
(d) 0.0256
(a) 0.6525.
(c) 0.8704
(b) 0.9744.​

Answer 1

Answer:

0.9744

Step-by-step explanation:

P(0)=4C0 (0.6)raised0 (0.4)raised to4=0.0256

P(atleast one passed) =1-P(nobody passed)

=1-P(0)

=0.9744

Answer 2

Given:

Percentage of success in an exam is 60

To Find:

Probability that out of 4 students in a group at least one has passed?

Solution:

Probability of success in exam = .60

Probability of failure = .40

Probability that atleast one student out of 4 passed =

P(1 pass 3 fail) + P(2 pass 2 fail) + P(3 pass 1 fail) + P(all four passed)

P(1 pass 3 fail ) = $(.6)(.4)(.4)(.4)= .0384$

P(2 pass 2 fail) = $(.6)(.6)(.4)(.4)$ =  .0576

P(3 pass 1 fail )= $(.6)(.6)(.6)(.4)=.0864$

P(all 4 passed)=$(.6)(.6)(.6)(.6)$= .1296

P(atleast one out of four passed)= $.384+.0576+.0864+.1296 = .312$

Probability that out of four students, atleast one has .312.