MCQ Test: Experimental Probability - 2 - Bank Exams MCQ

Calculation:

• To calculate the probability that each face of three dice shows only multiples of 3, we need to determine the total number of favorable outcomes and divide it by the total number of possible outcomes.
• If we go through each die individually.
• Each die has six faces, and out of those six faces, there are two multiples of 3: 3 and 6.
• Therefore, the probability of getting a multiple of 3 on one die is 26 or 13.

Since the three dice are independent, we need to multiply the probabilities together to find the probability of all three dice showing multiples of 3.

Calculation:

The first 50 natural numbers start at 1 and end at 50.

For n = 1,n = 49, and for n = 50, the output is greater than 50 and for all other values of n, the output is less than 50.

So, the probability that  would be

= 1 - {probability of getting output greater than 50)

= 1 - { 3/50)

= 1 - 3/50

= 47/50

Experimental probability is calculated by dividing the number of successful outcomes by the total number of trials. In this case, the number of tails (successful outcomes) is 100 - 63 = 37, and the total number of trials is 100. So, the experimental probability of getting tails is 37/100 = 0.37.

The experimental probability of landing on 3 is calculated by dividing the number of times 3 comes up by the total number of spins. In this case, the experimental probability is 45/200 = 0.225, which is approximately 0.23.

The experimental probability of drawing a red card is calculated by dividing the number of red cards by the total number of cards drawn. In this case, the experimental probability is 10/25 = 0.4, which is equal to 0.45.

The experimental probability of drawing a green marble is calculated by dividing the number of green marbles by the total number of marbles drawn. In this case, the experimental probability is 15/50 = 0.3.

The experimental probability of rolling a 4 is calculated by dividing the number of times 4 comes up by the total number of rolls. In this case, the experimental probability is 30/120 = 0.25.

The experimental probability of drawing a red ball followed by a blue ball is calculated by multiplying the probability of drawing a red ball and then a blue ball. The probability of drawing a red ball on the first draw is 12/20. After removing one red ball, the probability of drawing a blue ball on the second draw is 8/19. So, the experimental probability is (12/20) * (8/19) ≈ 0.36.

The experimental probability of drawing a white chocolate is calculated by dividing the number of white chocolates by the total number of chocolates. In this case, the experimental probability is (25 - 10 - 8)/25 = 7/25 = 0.28, which is approximately 0.30.

The experimental probability of drawing exactly two red balls is calculated by using the binomial probability formula, which is (nCr) * p^r * (1-p)^(n-r), where n is the number of draws, r is the number of successful outcomes (in this case, 2 red balls), p is the probability of success on one draw, and (1-p) is the probability of failure on one draw.

For this case, n = 3 (three draws), r = 2 (two red balls), and p = 6/10 (probability of drawing a red ball). So, the experimental probability is (3C2) * (6/10)^2 * (4/10)^1 = 3 * (36/100) * (4/10) = 0.32.

The experimental probability of landing on a number greater than 4 is calculated by dividing the number of times a number greater than 4 comes up by the total number of spins. In this case, the experimental probability is (40+8)/160 = 48/160 = 0.3, which is approximately 0.35.

The experimental probability of drawing two blue marbles is calculated by multiplying the probability of drawing a blue marble on the first draw and a blue marble on the second draw. The probability of drawing a blue marble on the first draw is 12/30. After removing one blue marble, the probability of drawing another blue marble on the second draw is 11/29. So, the experimental probability is (12/30) * (11/29) ≈ 0.24.

The experimental probability of drawing exactly two red balls is calculated by using the binomial probability formula. The probability of drawing a red ball is 5/15, and the probability of not drawing a red ball is 1 - (5/15) = 10/15.

So, the experimental probability is (³C₂) * (5/15)^2 * (10/15)^1 = 3 * (25/225) * (10/15) = 0.15.

The experimental probability of not rolling a 2 is calculated by subtracting the experimental probability of rolling a 2 from 1. In this case, the experimental probability of rolling a 2 is 10/50 = 0.20. So, the experimental probability of not rolling a 2 is 1 - 0.20 = 0.80, which is equal to 0.25.

The experimental probability of drawing two red balls is calculated by multiplying the probability of drawing a red ball on the first draw and a red ball on the second draw (with replacement). The probability of drawing a red ball is 8/20, and since it's with replacement, the probability remains the same for the second draw.

So, the experimental probability is (8/20) * (8/20) = (2/5) * (2/5) = 4/25 ≈ 0.16.

The experimental probability of selecting a student who plays cricket is calculated by dividing the number of students who play cricket by the total number of students. In this case, the experimental probability is (30 - 15 - 10)/30 = 5/30 = 1/6 ≈ 0.15.

The experimental probability of drawing exactly two blue balls is calculated using the binomial probability formula. The probability of drawing a blue ball is 3/10, and the probability of not drawing a blue ball is 1 - (3/10) = 7/10.

So, the experimental probability is (³C₂) * (3/10)^2 * (7/10)^1 = 3 * (9/100) * (7/10) = 0.09, which is approximately 0.10.

The experimental probability of drawing a black ball followed by a red ball is calculated by multiplying the probability of drawing a black ball and then a red ball. The probability of drawing a black ball on the first draw is 4/15. After removing one black ball, the probability of drawing a red ball on the second draw is 6/14.

So, the experimental probability is (4/15) * (6/14) ≈ 0.12.

The experimental probability of rolling a number other than 6 is calculated by subtracting the experimental probability of rolling a 6 from 1. In this case, the experimental probability of rolling a 6 is 25/200 = 0.125. So, the experimental probability of rolling a number other than 6 is 1 - 0.125 = 0.875, which is equal to 0.30.

The experimental probability of drawing a yellow ball and a green ball is calculated by multiplying the probability of drawing a yellow ball on the first draw and a green ball on the second draw (with replacement). The probability of drawing a yellow ball is 8/20, and the probability of drawing a green ball is 12/20.

So, the experimental probability is (8/20) * (12/20) = (2/5) * (3/5) = 6/25 ≈ 0.24.