Probability — Telangana (SSC) Class 9 Mathematics Solutions (Free)
Free step-by-step Telangana (SSC) Class 9 Mathematics solutions for "Probability" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Telangana (SSC) Class 9 Mathematics solutions for "Probability" — important questions with detailed answers, download PDF for board…
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Q1: A coin is tossed 100 times and heads appear 60 times. Find the empirical probability of getting heads.
Step 1: Number of trials = 100
Step 2: Number of times heads appear = 60
Step 3: Empirical probability = (Number of favorable outcomes)/(Total number of trials)
Step 4: P(heads) = 60/100 = 3/5 = 0.6
Final Answer: Empirical probability of heads = 0.6 or 60%
Q2: A die is rolled 120 times. The number 5 appears 28 times. Find the empirical probability of getting 5.
Step 1: Number of trials = 120
Step 2: Number of times 5 appears = 28
Step 3: Empirical probability P(5) = 28/120 = 7/30 ≈ 0.233
Final Answer: Empirical probability of getting 5 ≈ 0.233 or 23.3%
Q3: In a survey of 200 families, 85 have at least one car. Find the empirical probability that a randomly selected family has a car.
Step 1: Total number of families surveyed = 200
Step 2: Number of families with at least one car = 85
Step 3: Empirical probability P(car) = 85/200 = 17/40 = 0.425
Final Answer: Empirical probability = 0.425 or 42.5%
Q4: A bag contains 5 red, 3 blue, and 2 green balls. One ball is drawn 100 times with replacement. Red appears 52 times. Find empirical probability of red.
Step 1: Number of trials = 100
Step 2: Red appears = 52 times
Step 3: Empirical probability P(red) = 52/100 = 13/25 = 0.52
Step 4: Theoretical probability P(red) = 5/10 = 1/2 = 0.5
Step 5: Empirical and theoretical are close (difference due to chance)
Final Answer: Empirical probability = 0.52
Q5: A card is drawn from a standard deck 500 times with replacement. An ace appears 35 times. Find empirical probability of drawing an ace.
Step 1: Number of trials = 500
Step 2: Ace appears = 35 times
Step 3: Empirical probability P(ace) = 35/500 = 7/100 = 0.07
Step 4: Theoretical probability = 4/52 ≈ 0.077
Step 5: Empirical and theoretical are approximately equal
Final Answer: Empirical probability = 0.07 or 7%
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