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MCQ Test: Theoretical Probability - 1 - Bank Exams MCQ


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20 Questions MCQ Test Data Interpretation for Competitive Examinations - MCQ Test: Theoretical Probability - 1

MCQ Test: Theoretical Probability - 1 for Bank Exams 2024 is part of Data Interpretation for Competitive Examinations preparation. The MCQ Test: Theoretical Probability - 1 questions and answers have been prepared according to the Bank Exams exam syllabus.The MCQ Test: Theoretical Probability - 1 MCQs are made for Bank Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ Test: Theoretical Probability - 1 below.
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MCQ Test: Theoretical Probability - 1 - Question 1

A bag contains 8 blue balls and 4 green balls. Two balls are drawn at random without replacement. What is the probability of drawing a blue ball and then a green ball?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 1

When drawing without replacement, the probability of the first ball being blue is 8/12. After removing one blue ball, there are 7 blue balls left out of 11 balls in the bag. So, the probability of the second ball being green is 4/11. To find the probability of drawing a blue ball and then a green ball, multiply the individual probabilities: (8/12) * (4/11) = 32/132, which simplifies to 16/88.

MCQ Test: Theoretical Probability - 1 - Question 2

A fair six-sided die is rolled twice. What is the probability of getting a 5 on the first roll and an even number on the second roll?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 2

The probability of getting a 5 on the first roll of a fair six-sided die is 1/6. The probability of getting an even number on the second roll is 3/6 (there are three even numbers: 2, 4, and 6, out of a total of six possible outcomes). To find the probability of both events occurring, multiply the individual probabilities: (1/6) * (3/6) = 3/36, which simplifies to 1/12.

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MCQ Test: Theoretical Probability - 1 - Question 3

A bag contains 4 yellow balls and 6 green balls. Two balls are drawn at random without replacement. What is the probability of drawing two yellow balls?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 3

When drawing without replacement, the probability of the first ball being yellow is 4/10. After removing one yellow ball, there are 3 yellow balls left out of 9 balls in the bag. So, the probability of the second ball being yellow is 3/9. To find the probability of drawing two yellow balls, multiply the individual probabilities: (4/10) * (3/9) = 12/90, which simplifies to 2/15.

MCQ Test: Theoretical Probability - 1 - Question 4

A box contains 3 black balls and 5 white balls. If two balls are drawn at random with replacement, what is the probability of getting one black ball and one white ball?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 4

When drawing with replacement, the probability of the first ball being black is 3/8, and the probability of the first ball being white is 5/8. Since we are interested in either order (black and then white or white and then black), we need to consider both possibilities. To find the probability of getting one black ball and one white ball in any order, add the individual probabilities: (3/8) * (5/8) + (5/8) * (3/8) = 15/64.

MCQ Test: Theoretical Probability - 1 - Question 5

In a bag, there are 7 red balls and 5 blue balls. One ball is drawn at random. What is the probability of drawing a red ball or a blue ball?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 5

There are 7 red balls and 5 blue balls out of a total of 12 balls (7 red + 5 blue) in the bag. The probability of drawing a red ball or a blue ball is (7 + 5) / 12 = 12/12, which simplifies to 1.

MCQ Test: Theoretical Probability - 1 - Question 6

A bag contains 4 black balls and 6 white balls. Two balls are drawn at random without replacement. What is the probability of drawing two white balls in a row?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 6

When drawing without replacement, the probability of the first ball being white is 6/10. After removing one white ball, there are 5 white balls left out of 9 balls in the bag. So, the probability of the second ball being white is 5/9. To find the probability of drawing two white balls in a row, multiply the individual probabilities: (6/10) * (5/9) = 30/90, which simplifies to 2/15.

MCQ Test: Theoretical Probability - 1 - Question 7

A box contains 8 blue balls and 6 red balls. If two balls are drawn at random with replacement, what is the probability of getting two red balls?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 7

When drawing with replacement, the probability of the first ball being red is 6/14, and the probability of the second ball being red is also 6/14. To find the probability of getting two red balls, multiply the individual probabilities: (6/14) * (6/14) = 36/196, which simplifies to 9/49.

MCQ Test: Theoretical Probability - 1 - Question 8

A box contains 5 yellow balls and 7 orange balls. Two balls are drawn at random without replacement. What is the probability of drawing two balls of different colors?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 8

There are two ways to draw two balls of different colors: one yellow and one orange or one orange and one yellow. The probability of drawing one yellow and one orange ball is (5/12) * (7/11) = 35/132. The probability of drawing one orange and one yellow ball is (7/12) * (5/11) = 35/132. Summing up the probabilities of both cases: 35/132 + 35/132 = 70/132, which simplifies to 35/66.

MCQ Test: Theoretical Probability - 1 - Question 9

A spinner has 6 equal sections, each numbered from 1 to 6. What is the probability of landing on a number greater than 4?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 9

There are two numbers greater than 4 (5 and 6) out of six numbers (1 to 6) on the spinner. The probability of landing on a number greater than 4 is 2/6, which simplifies to 1/3.

MCQ Test: Theoretical Probability - 1 - Question 10

A bag contains 8 black balls and 6 white balls. If two balls are drawn at random with replacement, what is the probability of getting a black ball and a white ball in any order?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 10

When drawing with replacement, the probability of the first ball being black is 8/14, and the probability of the first ball being white is 6/14. Since we are interested in either order (black and then white or white and then black), we need to consider both possibilities. To find the probability of getting a black ball and a white ball in any order, add the individual probabilities: (8/14) * (6/14) + (6/14) * (8/14) = 48/196 + 48/196 = 96/196, which simplifies to 24/49.

MCQ Test: Theoretical Probability - 1 - Question 11

A box contains 6 red balls and 4 green balls. Two balls are drawn at random without replacement. What is the probability of drawing a red ball followed by a green ball?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 11

When drawing without replacement, the probability of the first ball being red is 6/10. After removing one red ball, there are 5 red balls left out of 9 balls in the box. So, the probability of the second ball being green is 4/9. To find the probability of both events occurring, multiply the individual probabilities: (6/10) * (4/9) = 24/90, which simplifies to 4/15.

MCQ Test: Theoretical Probability - 1 - Question 12

A bag contains 4 white balls, 6 red balls, and 5 blue balls. Two balls are drawn at random without replacement. What is the probability of drawing two balls of the same color?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 12

There are three possible ways to draw two balls of the same color: two white balls, two red balls, or two blue balls. The probability of drawing two white balls is (4/15) * (3/14) = 12/210. The probability of drawing two red balls is (6/15) * (5/14) = 30/210. The probability of drawing two blue balls is (5/15) * (4/14) = 20/210. Summing up the probabilities of all three cases: 12/210 + 30/210 + 20/210 = 62/210, which simplifies to 31/105.

MCQ Test: Theoretical Probability - 1 - Question 13

A bag contains 5 red balls and 7 blue balls. Two balls are drawn at random without replacement. What is the probability of drawing two blue balls?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 13

There are 7 blue balls out of a total of 12 balls (5 red + 7 blue) in the bag. When drawing without replacement, the probability of the first ball being blue is 7/12. After removing one blue ball, there are 6 blue balls left out of 11 balls in the bag. So, the probability of the second ball being blue is 6/11. To find the probability of both events occurring, multiply the individual probabilities: (7/12) * (6/11) = 42/132, which simplifies to 7/132.

MCQ Test: Theoretical Probability - 1 - Question 14

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 14

When flipping a fair coin, the probability of getting heads on a single flip is 1/2, and the probability of getting tails on a single flip is also 1/2. To get exactly two heads in three flips, there are three possible outcomes: HHT, HTH, and THH, where H represents heads and T represents tails. The probability of each outcome is (1/2) * (1/2) * (1/2) = 1/8. Since there are three favorable outcomes, the total probability of getting exactly two heads is 3/8.

MCQ Test: Theoretical Probability - 1 - Question 15

A box contains 10 red balls and 8 blue balls. If two balls are drawn at random with replacement, what is the probability of getting two red balls?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 15

When drawing with replacement, the probability of the first ball being red is 10/18 (10 red balls out of 18 total balls). After replacing the first ball, there are still 10 red balls out of 18 balls in the box. So, the probability of the second ball being red is also 10/18. To find the probability of both events occurring, multiply the individual probabilities: (10/18) * (10/18) = 100/324, which simplifies to 10/36.

MCQ Test: Theoretical Probability - 1 - Question 16

In a bag, there are 6 red balls, 4 blue balls, and 5 green balls. One ball is drawn at random. What is the probability of drawing a blue or a green ball?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 16

There are 4 blue balls and 5 green balls out of a total of 15 balls (6 red + 4 blue + 5 green) in the bag. The probability of drawing a blue or a green ball is (4 + 5) / 15 = 9/15, which simplifies to 3/5.

MCQ Test: Theoretical Probability - 1 - Question 17

A standard deck of cards contains 4 suits (hearts, diamonds, clubs, spades), each with 13 cards. What is the probability of drawing a heart or a diamond from the deck?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 17

There are 13 hearts and 13 diamonds out of a total of 52 cards in the deck. The probability of drawing a heart or a diamond is (13 + 13) / 52 = 26/52, which simplifies to 1/2.

MCQ Test: Theoretical Probability - 1 - Question 18

In a bag, there are 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability of both balls being red?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 18

There are 5 red balls out of a total of 8 balls (5 red + 3 blue) in the bag. When drawing without replacement, the probability of the first ball being red is 5/8. After removing one red ball, there are 4 red balls left out of 7 balls in the bag. So, the probability of the second ball being red is 4/7. To find the probability of both events occurring, multiply the individual probabilities: (5/8) * (4/7) = 20/56, which simplifies to 5/24.

MCQ Test: Theoretical Probability - 1 - Question 19

A class has 25 students: 15 girls and 10 boys. If a student is selected at random, what is the probability of selecting a boy?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 19

There are 10 boys out of a total of 25 students in the class. The probability of selecting a boy is 10/25, which simplifies to 2/5.

MCQ Test: Theoretical Probability - 1 - Question 20

A spinner is divided into 8 equal sections numbered from 1 to 8. What is the probability of landing on an even number?

Detailed Solution for MCQ Test: Theoretical Probability - 1 - Question 20

There are four even numbers (2, 4, 6, 8) out of eight numbers (1 to 8) on the spinner. The probability of landing on an even number is 4/8, which simplifies to 1/2.

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