Additional Maths Binomial Probability Quiz

Explanation
The probability of getting one question wrong is 3/4 (since there are 4 possible answers and she chooses one at random). Since there are 10 questions, the probability of getting all 10 wrong is (3/4)^10, which is approximately 0.0563.

Explanation
The probability that Sruthi gets exactly 9 wrong can be calculated using the binomial probability formula. Since there are 10 questions and each question has 4 possible answers, the probability of getting a question wrong is 3/4 and the probability of getting a question right is 1/4. To get exactly 9 wrong, Sruthi needs to get only one question right out of the 10. Therefore, the probability can be calculated as (10 choose 1) * (1/4)^1 * (3/4)^9 = 10 * 1/4 * (3/4)^9 = 0.188.

Explanation
The probability that Neha gets exactly 5 wrong can be calculated using the binomial probability formula. Since there are 10 questions and each question has 4 possible answers, the probability of getting a question wrong is 3/4. Therefore, the probability of getting exactly 5 wrong can be calculated as (10 choose 5) * (3/4)^5 * (1/4)^5 = 0.0584.

Explanation
The probability that Karishma gets at least 9 correct can be calculated by finding the probability of getting exactly 9 correct and the probability of getting all 10 correct, and then adding these probabilities together. The probability of getting exactly 9 correct is calculated by multiplying the probability of getting one question correct (1/4) by the probability of getting the other 9 questions incorrect (3/4) and then multiplying by the number of ways to arrange 9 correct answers in a set of 10 questions (10C9). The probability of getting all 10 correct is simply (1/4)^10. Adding these probabilities together gives a probability of approximately 0.756.

Explanation
The probability of choosing a non-faulty glass from the batch is 80% (1 - 20% = 80%). Since we are choosing 6 glasses at random, the probability of choosing a non-faulty glass for each selection is 0.8. To find the probability that none of the 6 chosen glasses are faulty, we multiply the probabilities together: 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8 = 0.262. Therefore, the probability that none of the 6 chosen glasses are faulty is 0.262.

Explanation
The probability of choosing exactly 2 faulty glasses out of 6 can be calculated using the binomial probability formula. The formula is P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the total number of trials (6), k is the number of successful outcomes (2), p is the probability of success (20% or 0.2), and (nCk) is the combination formula. Plugging in the values, we get P(X=2) = (6C2) * 0.2^2 * 0.8^4 = 15 * 0.04 * 0.4096 = 0.246.

Explanation
The probability of choosing a faulty glass from the batch is 20%. Since we are choosing 6 glasses at random, the probability of choosing exactly 4 faulty glasses can be calculated using the binomial probability formula. The formula is P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the total number of trials, k is the number of successful outcomes, p is the probability of success, and (nCk) represents the number of combinations. In this case, n=6, k=4, and p=0.2. Plugging these values into the formula, we get P(X=4) = (6C4) * 0.2^4 * (1-0.2)^(6-4) = 15 * 0.0016 * 0.64 = 0.0154. Therefore, the probability that exactly 4 out of the 6 chosen glasses are faulty is 0.0154.

Explanation
To find the probability that at least one out of six randomly chosen glasses is faulty, we can use the concept of complementary probability. The complementary probability is the probability that the opposite event occurs, in this case, the probability that none of the six chosen glasses are faulty.

The probability that a randomly chosen glass is not faulty is 1 - 0.20 = 0.80. Therefore, the probability that none of the six chosen glasses are faulty is 0.80^6 = 0.262.

The probability that at least one out of the six chosen glasses is faulty is equal to 1 minus the probability that none of them are faulty. So, the probability is 1 - 0.262 = 0.738.

Therefore, the correct answer is 0.738.

Explanation
The probability that at least 2 glasses are good can be calculated by finding the probability that exactly 0 or 1 glass is good and subtracting it from 1. To find the probability that exactly 0 glasses are good, we can calculate (0.2)^6 since each glass has a 20% chance of being faulty. To find the probability that exactly 1 glass is good, we can calculate 6*(0.2)^1*(0.8)^5 since there are 6 ways to choose which glass is good. Subtracting these probabilities from 1 gives us the probability that at least 2 glasses are good, which is approximately 0.998.