Probability-Event relations

Solution:

1. Identify the probabilities:

   • P(A) = 30/50 = 0.60

   • P(B) = 20/50 = 0.40

   • P(A \cup B) = 12/50 = 0.24

2. Apply the Additive Rule:

   P(A \cup B) = P(A) + P(B) - P(A \cap B)
   = 0.60 + 0.40 - 0.24 = 0.76

   Final Answer: There is a 76% chance the student uses at least one of the two devices.

Solution:

1. Identify the probabilities:

   • P(A) = 30/50 = 0.60

   • P(C) = 10/50 = 0.20

2. Determine Relationship: Since no student uses both, these events are Mutually Exclusive ((A \cap C) = 0).

3. Apply the Rule for Mutually Exclusive Events:

   P(A \cup C) = P(A) + P(C)

   = 0.60 + 0.20 = 0.80

   Final Answer: There is an 80% chance the student uses one of these two phone types.

Solution:

1. Identify the Event: The event "neither" is the Complement of the Union.

2. Apply the Complement Rule:

   P(Neither) = 1 - P(A \cup B)

   P(Neither) = 1 - 0.76 = 0.24

   Final Answer: There is a 24% chance the student uses neither device.