Mathematics Multiple Choice Questions on “Probability – Independent Events”.
1. Events P and Q are independent if P(A∩B) = P(A) P(B).
a) False
b) True
Answer: b
Clarification: According to the definition of independent events,
P(A/B) = P(A)
P(A ∩ B) ⁄ P(B) = P(A) or P(A ∩ B) = P(A) P(B). Here, P(B) ≠ 0.
2. What are independent events?
a) If the outcome of one event does not affect the outcome of another
b) If the outcome of one event affects the outcome of another
c) Any one of the outcomes of one event does not affect the outcome of another
d) Any one of the outcomes of one event does affect the outcome of another
Answer: a
Clarification: Independent events refer to the outcome of one event does not affect the outcome of another. For example, if two persons participating in two different races, winning one person doesn’t affect the winning of another person.
3. A dice is thrown twice, what is the probability of getting two 3’s?
a) (frac {1}{66})
b) (frac {1}{16})
c) (frac {1}{36})
d) (frac {1}{36})
Answer: d
Clarification: Probability of getting 3 in the first throw = (frac {1}{6})
Probability of getting of 3 in the second throw = (frac {1}{6})
Total probability = (frac {1}{6} times frac {1}{6} = frac {1}{36})
4. What is the formula for independent events?
a) P(AB) = P(A) P(B)
b) P(A∩B) = P(A) P(B)
c) P(A+B) = P(A) P(B)
d) P(A-B) = P(A) P(B)
Answer: b
Clarification: Independent events refer to the outcome of one event does not affect the outcome of another. The formula for independent events are P(A∩B) = P(A) P(B).
5. What is the probability of obtaining 4 heads in a row when a coin is tossed?
a) (frac {5}{8})
b) (frac {6}{19})
c) (frac {1}{16})
d) (frac {4}{7})
Answer: c
Clarification: Probability of getting 4 heads in a row = (frac {1}{2} times frac {1}{2} times frac {1}{2} times frac {1}{2} = frac {1}{16})
hence, the probability of getting 4 heads in a row = (frac {1}{16})
6. A bag contains a pair of gloves in colours blue, red, yellow and pink. You reach into the
bag and choose a pair of gloves without looking. You replace this pair and then choose another pair of gloves. What is the probability that you will choose the pink pair of gloves both times?
a) (frac {3}{7})
b) (frac {4}{7})
c) (frac {1}{16})
d) (frac {1}{7})
Answer: c
Clarification: Probability of pink = (frac {1}{4})
Probability of choosing pink pair of gloves twice = (frac {1}{4} times frac {1}{4} = frac {1}{16})
7. A box contains a pair of socks in colours blue, red, yellow, green and pink. You reach into the box and choose a pair of socks without looking. You replace this pair and then choose another pair of socks. What is the probability that you will choose the yellow pair of socks both times?
a) (frac {8}{11})
b) (frac {1}{25})
c) (frac {4}{11})
d) (frac {7}{4})
Answer: b
Clarification: Probability of yellow = (frac {1}{5})
Probability of choosing pink pair of gloves twice = (frac {1}{5} times frac {1}{5} = frac {1}{25})
8. What is the probability of a coin landing on the tail and the dice showing 2 when a coin is tossed and dice is thrown?
a) (frac {1}{12})
b) (frac {8}{10})
c) (frac {7}{1})
d) (frac {4}{11})
Answer: a
Clarification: The probability of coin landing on the tail = (frac {1}{2})
The probability of the dice showing 2 = (frac {1}{6})
Total probability = (frac {1}{2} times frac {1}{6} = frac {1}{12})
9. A card is chosen at random from a deck of cards and then replaced, a second card is chosen. What is the probability of choosing a four and then a queen?
a) (frac {7}{11})
b) (frac {7}{100})
c) (frac {1}{169})
d) (frac {9}{11})
Answer: c
Clarification: The probability of drawing a four = (frac {4}{52})
The probability of drawing a queen = (frac {4}{52})
Total probability = (frac {4}{52} times frac {4}{52} = frac {1}{169} )
10. A bag contains 4 red, 2 green and 7 blue balls. What is the probability of drawing a red ball and the first ball drawn is blue? The balls drawn are replaced in the bag.
a) (frac {28}{169})
b) (frac {8}{11})
c) (frac {4}{128})
d) (frac {14}{11})
Answer: a
Clarification: Total number of balls = 4 + 2 + 7 = 13
The probability of the first ball to be blue = (frac {7}{13})
The probability of drawing red ball as the second ball = (frac {4}{13})
Total probability = (frac {7}{13} times frac {4}{13} = frac {28}{169})
11. A bag contains 3 red, 2 white and 4 green balls. What is the probability of drawing the second ball to be white and the first ball drawn is green? The balls are replaced in the bag.
a) (frac {1}{9})
b) (frac {2}{9})
c) (frac {8}{81})
d) (frac {2}{81})
Answer: c
Clarification: Total number of balls = 9
The probability of the first ball to be white = (frac {2}{9})
The probability of drawing green ball for the second time with replacement = (frac {4}{9})
Total probability = (frac {2}{9} times frac {4}{9} = frac {8}{81})
12. A bag contains 3 red, 2 white and 4 green balls. What is the probability of drawing the second ball to be green if the first ball drawn is red? The balls are replaced in the bag.
a) (frac {3}{9})
b) (frac {4}{27})
c) (frac {4}{3})
d) (frac {4}{17})
Answer: b
Clarification: Total number of balls = 9
The probability of the first ball to be red = (frac {3}{9})
The probability of the second ball to be green with replacement = (frac {4}{9})
Total probability = (frac {3}{9} times frac {4}{9} = frac {4}{27})