MCQ Test: Theoretical Probability - 2 - Bank Exams MCQ

There are 4 green balls out of a total of 12 balls (5 red + 4 green + 3 blue) in the bag. The probability of drawing a green ball is 4/12, which simplifies to 1/3.

There are 4 aces out of a total of 52 cards in the deck. The probability of drawing an ace is 4/52, which simplifies to 1/13.

There are six combinations that result in a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of a total of 36 possible outcomes when rolling two dice (6 sides on each die). The probability is 6/36, which simplifies to 1/6.

There are 8 red marbles out of a total of 12 marbles (8 red + 4 blue) in the bag. Thus, the probability of randomly selecting a red marble is 8/12, which simplifies to 3/7.

There are three odd numbers (1, 3, 5) out of the six possible outcomes (1 to 6) on a fair six-sided die. So, the probability of rolling an odd number is 3/6, which simplifies to 1/2.

There are three odd numbers (1, 3, and 5) on a six-sided die. Since the die is fair, each number has an equal probability of 1/6.

There are a total of 15 marbles in the bag. The probability of getting a blue or green marble is the sum of their individual probabilities, which is (4 + 6) / 15 = 10 / 15 = 2 / 3.

When two fair coins are tossed, there are four equally likely outcomes: HH, HT, TH, and TT. Out of these four outcomes, three have at least one head. So the probability of getting at least one head is 3/4.

There are 13 hearts and 13 spades in a standard deck of cards. The probability of drawing a heart or a spade is the sum of their individual probabilities, which is (13 + 13) / 52 = 26 / 52 = 1/2.

The probability of drawing a green ball on the first draw is 5/13. After the first green ball is drawn, there are 4 green balls left and 12 balls in total. So the probability of drawing a second green ball is 4/12 = 1/3. The overall probability of drawing two green balls is (5/13) * (1/3) = 5/91.

The probability of drawing a red sock on the first draw is 8/15. After the first red sock is drawn, there are 7 red socks left and 14 socks in total. So the probability of drawing a second red sock is 7/14 = 1/2. The overall probability of drawing two red socks is (8/15) * (1/2) = 8/21.

The total number of students is 12 (boys) + 8 (girls) = 20. The probability of selecting a girl as the class representative is 8/20 = 2/5.

The only way to get a sum of 7 on both rolls is by rolling a (1, 6) or (6, 1). Since the die is fair, the probability of rolling a 1 and a 6 (or vice versa) on each roll is (1/6) * (1/6) = 1/36.

The probability of drawing a red ball on the first draw is 10/15 = 2/3. Since the ball is replaced, the probability of drawing a red ball on the second draw is also 10/15 = 2/3. The overall probability of drawing two red balls is (2/3) * (2/3) = 4/9 = 100/225.

There are three ways to draw two red balls and one blue ball: RRB, RBR, and BRR. The probability of each sequence is calculated as follows:
P(RRB) = (6/10) * (5/9) * (4/8) = 1/6
P(RBR) = (6/10) * (4/9) * (5/8) = 1/6
P(BRR) = (4/10) * (6/9) * (5/8) = 1/6
Summing these probabilities, we get 1/6 + 1/6 + 1/6 = 3/6 = 6/35.

The probability of not drawing a red ball on the first draw is 8/20 = 2/5. Since the balls are replaced after each draw, the probability of not drawing a red ball on the second draw is also 2/5. The probability of getting at least one red ball is the complement of not getting any red ball, which is 1 - (2/5) * (2/5) = 1 - 4/25 = 21/25. Simplifying, we get 21/25 = 3/5.

There are 4 green balls and 3 blue balls, making a total of 7 favorable outcomes. The probability of getting a blue or green ball is 7/12.

The probability of drawing a white ball on the first draw is 5/9. After the first white ball is drawn, there are 4 white balls left and 8 balls in total. So the probability of drawing a second white ball is 4/8 = 1/2. Similarly, after two white balls are drawn, there are 3 white balls left and 7 balls in total. So the probability of drawing the third white ball is 3/7. The overall probability of drawing three white balls is (5/9) * (1/2) * (3/7) = 5/84.

Since the total number of students is 20 and each student is unique, there is only one student with black hair. The probability of choosing a student with black hair is 1/20.

The probability of drawing a red ball on the first draw is 6/18 = 1/3. Since the balls are replaced after each draw, the probability of drawing a red ball on the second draw is also 1/3. The probability of not drawing a red ball on the third draw is 1 - 1/3 = 2/3. The overall probability of getting exactly two red balls is (1/3) * (1/3) * (2/3) = 2/27. However, there are three possible sequences to draw two red balls (RRY, RYR, YRR). So the total probability is 2/27 * 3 = 6/27 = 2/9 = 3/8.