Question

1.If I choose a sample of 7 (7 trials), what is the probability that:

i. Exactly 1 of seven passes?

ii. 3 or less pass?

iii. All seven pass?

What if we have a sample of 15 (15 trials)? What is the probability that:

1. Exactly 3 of the 15 pass?
2. Less than 7 pass? More than 6 pass?
3. All pass?

You have a true false test with ten questions and you need more than 60 to pass.

1. What is probability that you pass?
2. What is the probability that you pass a ten question test multiple choice with three possible answers?
3. Suppose now you have a 5 question true false test. What is the probability that you pass?
4. Now you have a 20 question test with four possible answer. What is the probability that you pass?

Answer 1

(Since there are more than 4 parts i will answer first 4, i.e 1.(i)(ii)(iii), 2.(i))

let probability of passing in one trial = p

probability in binomial distribution :

1.

x=no. of pass

n=7

(i)

P(1) = (7C1)*(p^1)*((1-p)^6)

P(1) = 7*(p^1)*((1-p)^6)

(ii)

P(x<=3) = P(0)+P(1)+P(2)+P(3)

P(x<=3) = (7C0)*(p^0)*((1-p)^7) + (7C1)*(p^1)*((1-p)^6)+ (7C2)*(p^2)*((1-p)^5) + (7C3)*(p^3)*((1-p)^4)

(iii)

P(7) = (7C7)*(p^7)*((1-p)^0)

P(7) = p^7

2.

n=15

(i)

P(3) = (15C3)*(p^3)*((1-p)^12)

P.S. (please upvote if you find the answer satisfactory)