Example 1: Tossing a Fair Coin

Problem: A coin is tossed 100 times.

How many times would you expect it to land on heads?

Solution:

• Step 1: Probability of heads = 0.5 (since the coin is fair).
• Step 2: Total number of trials = 100.
• Step 3: Expected frequency = 0.5 × 100 = 50

Answer: The expected frequency of getting heads is 50.

Example 2: Rolling a Die

Problem: A six-sided die is rolled 120 times.

How many times would you expect to roll a 4?

Solution:

• Step 1: Probability of rolling a 4 = 1/6
• Step 2: Total number of trials = 120.
• Step 3: Expected frequency = 1/6 × 120 = 20

Answer: The expected frequency of rolling a 4 is 20.

Example 3: Real-World Application (Traffic Lights)

Problem: In a survey, it's found that 30% of vehicles at an intersection run a red light. If 500 vehicles pass through the intersection, how many would you expect to run a red light?

Solution:

• Step 1: Probability of running a red light = 0.3.
• Step 2: Total number of trials = 500.
• Step 3: Expected frequency = 0.3 × 500 = 150

Answer: The expected frequency of vehicles running a red light is 150.