# Probability and Statistics - Online Test

Q1.
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If two stones are picked at random, what is the probability that both are blue?
Explaination / Solution:

Probability if both is blue
4C2/12C2 = 6/66 → 1/11

Q2.
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If four balls are picked at random, what is the probability that two are blue and two are red?
Explaination / Solution:

Probability if two are Blue and two are Red
[(4C2*5C2)/12C4] = (6*10)/495 → 4/33

Q3.
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If three balls are picked at random, what is the probability that at least one is green?
Explaination / Solution:

Probability if at least one is Green
[1-(9C3/12C3)] = 84/220 → 34/55

Q4.
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If two balls are picked at random, what is the probability that either both are red or both are blue?
Explaination / Solution:

Probabilities if both either are Red or either are blue
= (5C2 + 4C2)/12C2 = (10+6)/66 → 8/33

Q5.
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If four balls are picked at random, what is the probability that two are blue, one is green and one is red?
Explaination / Solution:

Probabilities if two are blue and one is green and one is red
= [(4C2*3C1*5C1)/ 12C4] = (6*3*5)/(495) = 2/11

Q6.
Direction: Study the given information carefully and answer the questions that follow—
A store contains 4 red, 5 blue, 4 green shirts.
If two shirts are picked at random, what is the probability that both are green?
Explaination / Solution:

Probabilities if both are green
4C2/13C2 = 6/78 → 1/13

Q7. If three shirts are picked at random, what is the probability that two are blue and one is red?
Explaination / Solution:

Probability if two are Blue and one are Red
[(5C2*4C1)/13C3] = (10*4)/286 → 20/143

Q8. If two shirts are picked at random, what is the probability that at least one is green?
Explaination / Solution:

Probability if at least one is Green
[1-(9C2/13C2)] = 42/78 → 7/13

Q9. If two shirts are picked at random, what is the probability that either both are red or both are green?
Explaination / Solution:

Probabilities if both either are Red or either are green
(4C2 + 4C2)/13C2 = (6+6)/78 → 2/13

Q10. If two shirts are picked at random, what is the probability that at most one is blue,?
Explaination / Solution:

Probabilities if at most one is blue =
[(5C0*8C25C1*8C1)/ 13C2] = (1*28 + 5*8)/(78) = 34/39