Probability and Statistics - Online Test
Q1. If three shirts are picked at random, what is the probability that two are blue and one is red?
Answer : Option C
Explaination / Solution:
Probability if two are Blue and one are Red
[(5C2*4C1)/13C3] = (10*4)/286 → 20/143
Q2. Coefficient of correlation between the observations ( 1, 6 ) , ( 2 , 5 ) , ( 3 , 4) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) is
Answer : Option A
Explaination / Solution:
use,r(x,y)=1n∑i=1n(Xi−X¯)(Yi−Y¯)1n∑i=1n(Xi−X¯)2√1n∑i=1n(Yi−Y¯)2√
Q3. If A and B are events such that P(A|B) = P(B|A), then
Answer : Option B
Explaination / Solution:
It is given that :
Q4. If two shirts are picked at random, what is the probability that at least one is green?
Answer : Option B
Explaination / Solution:
Probability if at least one is Green
[1-(9C2/13C2)] = 42/78 → 7/13
Q5. If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρ satisfies.
Answer : Option A
Explaination / Solution:
No Explaination.
Q6. If E and F are independent, then
Answer : Option A
Explaination / Solution:
we know that
If E and F are independent, then P(E/F) = P(E) and P(F/E) = P(F)
P (E ∩ F) = P (E) P (F).
Q7. If two shirts are picked at random, what is the probability that either both are red or both are green?
Answer : Option A
Explaination / Solution:
Probabilities if both either are Red or either are green
(4C2 + 4C2)/13C2 = (6+6)/78 → 2/13
Q8. If two shirts are picked at random, what is the probability that at most one is blue,?
Answer : Option C
Explaination / Solution:
Probabilities if at most one is blue =
[(5C0*8C2+ 5C1*8C1)/ 13C2] = (1*28 + 5*8)/(78) = 34/39
Q9. For a moderately skewed distribution, quartile deviation and the standard deviation are related by
Answer : Option D
Explaination / Solution:
its a standard result
Q10. If E and F are independent, then
Answer : Option A
Explaination / Solution:
If E and F are independent, then P (E|F) = P (E), P (F) ≠ 0 .
