Question

assume that 50% of all engineering students are good in mathematics determine the probability that among 18 exactly 10 are good at mathematics​

Answer 1

Answer:

3 /50=0.o6

Step-by-step explanation:

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Answer 2

Probability that 10 students are good in mathematics  out of  18  students  is $2431 (\frac{1}{2} )^{18}$ .

Step-by-step explanation:

Given:

Engineering students who good in mathematics are 50%.

To Find: Probability that 10 students are good in mathematics  out of  18  students.

Formula Used:

Bernoulli distribution is given by:

P(X=k)=nCk $p^{k} q^{n-k}$  ----------------------------- formula no.01

Here, P(X=k) = The probability of getting k students are good in mathematics  out of  n   engineering students .

n = number of  engineering  student.

X=  a random variable which consider value of k.

k = number of getting good student in mathematics.

p = probability of getting one student good in mathematics.

q = probability of not getting one student good in mathematics.

As given - Engineering students who good in mathematics are 50%.

p = probability of getting one  student good in mathematics  out of 100 student.

= 50/100 = 1/2

q= probability of not getting one  student good in mathematics  out of 100 student.

q= 1-p

=1-1/2 =1/2

n = 18 and k=10

Putting the value of n ,p, q and k in formula no.01.

P(X=10)=18C10 $(\frac{1}{2} )^{10} (\frac{1}{2} )^{18-10}$

            $=\frac{18!}{(18-10)! 10!)} (\frac{1}{2} )^{10} (\frac{1}{2} )^{8}$

            $=\frac{18!}{8! 10!)} (\frac{1}{2} )^{18}$

            $= 2431 (\frac{1}{2} )^{18}$

Thus, probability that 10 students are good in mathematics  out of  students  is $2431 (\frac{1}{2} )^{18}$ .