Final answer:
The probability that Amandeep's mother will serve either rice or carrots for dinner is 86%. This is calculated by finding P(A AND B) with the formula 1 = P(A) + P(B) - P(A AND B) + P(neither) and then applying it to P(A OR B) = P(A) + P(B) - P(A AND B).
Step-by-step explanation:
The question revolves around finding the probability that Amandeep's mother will serve either rice or carrots for dinner. To find the probability of either event happening, we use the formula P(A OR B) = P(A) + P(B) - P(A AND B). However, we are not directly given the probability of both rice and carrots being served together (P(A AND B)). Instead, we have the probabilities of rice (P(A)=0.73) and carrots (P(B)=0.30) being served and the probability of neither being served (P(neither)=0.14).
To find P(A AND B), we can use the fact that all probabilities must add up to 1. Hence, 1 = P(A) + P(B) - P(A AND B) + P(neither). Substituting the known values gives us 1 = 0.73 + 0.30 - P(A AND B) + 0.14. Solving for P(A AND B), we get P(A AND B) = 0.73 + 0.30 + 0.14 - 1, which is equal to 0.17.
With P(A AND B) found, we can then determine P(A OR B). So, P(A OR B) = 0.73 + 0.30 - 0.17 = 0.86. Therefore, there is an 86% chance that Amandeep's mother will serve either rice or carrots for dinner.