Question

ERROR ANALYSIS Events A and B are independent.

Describe and correct the error in finding P(A and B).
X
P(4)=0.6
P(B) = 0.2
P(A and B) = 0.6 +0.2=0.8

Answer 1

The error in the problem is the use of addition instead of multiplication when finding the probability of independent events occurring together. The correct method is P(A and B) = P(A) × P(B).

Step-by-step explanation:

The error in the calculation of P(A and B) is that the addition rule was incorrectly applied to independent events. For independent events, the correct method to find the joint probability is to multiply the probabilities of the two events, not add them. Therefore, the correct calculation for P(A and B), given that events A and B are independent, should be:

P(A and B) = P(A) × P(B)

For example, if the probability of learning Spanish (event A) is 0.4 and the probability of learning German (event B) is 0.2, then the probability of learning both Spanish and German is:

P(A and B) = 0.4 × 0.2 = 0.08

Thus, events A and B are indeed independent because the product of their individual probabilities equals the joint probability, fulfilling the property of independent events.