Final answer:
The probability that a student will get an A OR a B is approximately 0.425. The probability that a student will get an A OR a B OR a C is approximately 0.457. The probability that a student will get a grade lower than a C is approximately 0.543.
Step-by-step explanation:
To find the probability that a student will get an A OR a B, we need to add the probabilities of getting an A and getting a B, and then subtract the probability of getting both grades at the same time. So, P(A OR B) = P(A) + P(B) - P(A AND B). Given that P(A) = 0.29 and P(B) = 0.19, we can calculate the probability:
P(A OR B) = 0.29 + 0.19 - (P(A) * P(B)) = 0.48 - (0.29 * 0.19) = 0.48 - 0.0551 = 0.4249, or approximately 0.425.
To find the probability that a student will get an A OR a B OR a C, we need to add the probabilities of getting an A, getting a B, and getting a C, and then subtract the probabilities of getting any combination of two grades at the same time. So, P(A OR B OR C) = P(A) + P(B) + P(C) - P(A AND B) - P(A AND C) - P(B AND C) + P(A AND B AND C). Given the probabilities mentioned, we can calculate the probability:
P(A OR B OR C) = 0.29 + 0.19 + 0.23 - (P(A) * P(B)) - (P(A) * P(C)) - (P(B) * P(C)) + (P(A) * P(B) * P(C)) = 0.64 - (0.29 * 0.19) - (0.29 * 0.23) - (0.19 * 0.23) + (0.29 * 0.19 * 0.23) = 0.64 - 0.0551 - 0.0667 - 0.0437 + 0.00256 = 0.45706, or approximately 0.457.
To find the probability that a student will get a grade lower than a C, we need to subtract the probability of getting a C or higher from 1. So, P(grade < C) = 1 - P(A OR B OR C) = 1 - 0.45706 = 0.54294, or approximately 0.543.