4. Probability
Basic Concepts of Probability
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If the probability of an event is 20%, what is the expected number of times the event will occur in 90 independent trials?
A
72
B
18
C
9
D
20
Verified step by step guidance1
Step 1: Understand the concept of expected value. The expected value in probability is calculated as the product of the probability of an event and the number of trials. It represents the average number of occurrences of the event over a large number of trials.
Step 2: Identify the given values in the problem. The probability of the event occurring is 20%, which can be expressed as 0.2 in decimal form. The number of independent trials is 90.
Step 3: Write the formula for expected value. The formula is: , where is the expected value, is the probability of the event, and is the number of trials.
Step 4: Substitute the given values into the formula. Replace with 0.2 and with 90 in the formula.
Step 5: Multiply the probability (0.2) by the number of trials (90) to calculate the expected value. This will give the average number of times the event is expected to occur in 90 trials.
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