Final answer:
The probability that all three awards will go to a student from school B is 0.1113 (rounded to four decimal places).
Step-by-step explanation:
To find the probability that all three awards will go to a student from school B, we need to consider the total number of students competing from both schools and the number of students from school B. There are 10 students from school A and 12 students from school B, making a total of 22 students. The probability can be found by dividing the number of students from school B by the total number of students:
P(First place from B AND Second place from B AND Third place from B) = P(First place from B) x P(Second place from B) x P(Third place from B)
P(First place from B) = Number of students from school B / Total number of students = 12 / 22
The same reasoning and calculation apply to P(Second place from B) and P(Third place from B). Therefore, the probability that all three awards will go to a student from school B is:
P(First place from B) x P(Second place from B) x P(Third place from B) = (12/22) x (11/21) x (10/20) = 0.1113 (rounded to four decimal places).