Mathematics Questions and Answers – Probability – Independent Events

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Probability – Independent Events”.

1. Events P and Q are independent if P(A∩B) = P(A) P(B).
a) False
b) True
View Answer

Answer: b
Explanation: 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.
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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
View Answer

Answer: a
Explanation: 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) \(\frac {1}{36}\)
View Answer

Answer: d
Explanation: 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 = \(\frac {1}{6} \times \frac {1}{6} = \frac {1}{36}\)
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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)
View Answer

Answer: b
Explanation: 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) \(\frac {4}{7}\)
View Answer

Answer: c
Explanation: 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 = \(\frac {1}{16}\)
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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) \(\frac {1}{7}\)
View Answer

Answer: c
Explanation: 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) \(\frac {7}{4}\)
View Answer

Answer: b
Explanation: Probability of yellow = \(\frac {1}{5}\)
Probability of choosing pink pair of gloves twice = \(\frac {1}{5} \times \frac {1}{5} = \frac {1}{25}\)
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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) \(\frac {4}{11}\)
View Answer

Answer: a
Explanation: 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) \(\frac {9}{11}\)
View Answer

Answer: c
Explanation: The probability of drawing a four = \(\frac {4}{52}\)
The probability of drawing a queen = \(\frac {4}{52}\)
Total probability = \(\frac {4}{52} \times \frac {4}{52} = \frac {1}{169} \)
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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) \(\frac {14}{11}\)
View Answer

Answer: a
Explanation: 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) \(\frac {2}{81}\)
View Answer

Answer: c
Explanation: 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) \(\frac {4}{17}\)
View Answer

Answer: b
Explanation: 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 = \(\frac {3}{9} \times \frac {4}{9} = \frac {4}{27}\)

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter