Final answer:
The probability that a randomly selected participant brought both a microwave and a video game console (P(M and C)) is calculated by constructing a two-way table and solving for the number of students who brought both items. The final calculation shows the probability is 0.51.
Step-by-step explanation:
To solve this problem, we need to organize the given information into a two-way table (or contingency table) and then calculate the probability of a student bringing both a microwave and a video game console, represented as P(M and C).
Let's construct a two-way table based on the information provided:
Microwave (M)No MicrowaveConsole (C)xNo Console50
Adding up the students who brought microwaves (425), consoles (380), and neither (50) gives us a total that exceeds 500, which suggests some students brought both items. To find the overlap, we use the principle that the sum of the separate groups minus the overlap plus neither should equal the total number of students:
425 (microwaves) + 380 (consoles) - x (both) + 50 (neither) = 500
Solving for x gives:
x = 425 + 380 - 50 - 500 = 255
Now we replace x in our table:
Microwave (M)No MicrowaveConsole (C)255No Console50
The probability that a student brought both a microwave and a console P(M and C) is calculated by dividing the number of students who brought both items by the total number of students:
P(M and C) = 255 / 500 = 0.51