Probability — Karnataka (SSLC) Class 9 Mathematics Solutions (Free)
Free step-by-step Karnataka (SSLC) Class 9 Mathematics solutions for "Probability" — important questions with detailed answers, download PDF for board exam preparation.
✓ 100% Free
✓ No Login Needed
✓ NCERT / CBSE Aligned
✓ Download as PDF
TL;DR: Free step-by-step Karnataka (SSLC) Class 9 Mathematics solutions for "Probability" — important questions with detailed answers, download PDF for board…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
🤖 Stuck on any question? Ask Syllab's free AI Tutor for a step-by-step explanation — instant, unlimited, no login.
Probability — Textbook Questions Answered (8)
Q1: A coin is tossed 200 times. Heads appeared 110 times. What is the empirical probability of getting tails in a single toss?
Step 1: Total number of tosses = 200.
Step 2: Number of heads = 110.
Step 3: Number of tails = Total tosses - Number of heads = 200 - 110 = 90.
Step 4: Empirical probability of tails = Number of favorable outcomes / Total number of outcomes = 90 / 200.
Step 5: Simplify: 90/200 = 9/20 = 0.45.
Final Answer: The empirical probability of getting tails is 9/20 or 0.45.
Q2: A die is rolled 300 times and the following frequencies are observed: 1 appears 48 times, 2 appears 52 times, 3 appears 51 times, 4 appears 49 times, 5 appears 50 times, 6 appears 50 times. Find the empirical probability of rolling a number greater than 4.
Step 1: Total number of rolls = 300.
Step 2: Numbers greater than 4 are: 5 and 6.
Step 3: Frequency of rolling 5 = 50 times.
Step 4: Frequency of rolling 6 = 50 times.
Step 5: Total frequency of rolling a number greater than 4 = 50 + 50 = 100.
Step 6: Empirical probability of rolling a number greater than 4 = 100 / 300 = 1/3 ≈ 0.333.
Final Answer: The empirical probability of rolling a number greater than 4 is 1/3 or approximately 0.333.
Q3: A bag contains red and black balls. An experiment of drawing a ball (with replacement) is performed 150 times. Red ball was drawn 90 times. What is the empirical probability of drawing a black ball?
Step 1: Total number of draws = 150.
Step 2: Number of times red ball was drawn = 90.
Step 3: Number of times black ball was drawn = Total draws - Red draws = 150 - 90 = 60.
Step 4: Empirical probability of drawing black ball = 60 / 150 = 2/5 = 0.4.
Final Answer: The empirical probability of drawing a black ball is 2/5 or 0.4.
Q4: A spinner with 4 equal sections (colored Red, Blue, Green, Yellow) is spun 400 times. The results are: Red 95 times, Blue 110 times, Green 98 times, Yellow 97 times. Find the empirical probability of spinning Red or Blue.
Step 1: Total number of spins = 400.
Step 2: Number of times Red appeared = 95.
Step 3: Number of times Blue appeared = 110.
Step 4: Number of times Red or Blue appeared = 95 + 110 = 205.
Step 5: Empirical probability of Red or Blue = 205 / 400 = 41/80 = 0.5125.
Step 6: Theoretical probability of Red or Blue = 2/4 = 1/2 = 0.5 (equal sections).
Step 7: Empirical probability (0.5125) is close to theoretical probability (0.5).
Final Answer: The empirical probability of spinning Red or Blue is 41/80 or approximately 0.5125.
Q5: In a survey of 500 students, 320 prefer online learning while 180 prefer offline learning. Based on this data, what is the empirical probability that a randomly selected student prefers offline learning?
Step 1: Total number of students surveyed = 500.
Step 2: Number of students who prefer offline learning = 180.
Step 3: Empirical probability = Number of favorable outcomes / Total outcomes = 180 / 500.
Step 4: Simplify: 180/500 = 18/50 = 9/25 = 0.36.
Final Answer: The empirical probability that a randomly selected student prefers offline learning is 9/25 or 0.36.
Q6: A weather station records rainfall data for 365 days in a year. It rained on 145 days. What is the empirical probability that it will rain on any given day?
Step 1: Total number of days = 365.
Step 2: Number of days it rained = 145.
Step 3: Empirical probability of rain = 145 / 365.
Step 4: Simplify: 145/365 = 29/73 ≈ 0.397.
Final Answer: The empirical probability that it will rain on any given day is 29/73 or approximately 0.397.
Q7: A manufacturing company tests 1000 light bulbs. 950 bulbs work properly while 50 bulbs are defective. Find the empirical probability that a randomly selected bulb is defective.
Step 1: Total number of light bulbs tested = 1000.
Step 2: Number of defective bulbs = 50.
Step 3: Empirical probability of defective bulb = 50 / 1000.
Step 4: Simplify: 50/1000 = 1/20 = 0.05.
Final Answer: The empirical probability that a randomly selected bulb is defective is 1/20 or 0.05 (5%).
Q8: Cards numbered 1 to 50 are placed in a box. A card is drawn at random with replacement, 200 times. The card with number divisible by 5 (i.e., 5, 10, 15, 20, 25, 30, 35, 40, 45, 50) was drawn 38 times. Find the empirical probability of drawing a card with a number divisible by 5.
Step 1: Total number of draws (with replacement) = 200.
Step 2: Number of times a card divisible by 5 was drawn = 38.
Step 3: Empirical probability = 38 / 200 = 19/100 = 0.19.
Step 4: Theoretical probability = Number of cards divisible by 5 / Total cards = 10 / 50 = 1/5 = 0.2.
Step 5: Empirical probability (0.19) is close to theoretical probability (0.2).
Final Answer: The empirical probability of drawing a card with number divisible by 5 is 19/100 or 0.19.
Related
- Constructions — more Karnataka (SSLC) Class 9 Mathematics.
- Areas of Parallelograms and Triangles — more Karnataka (SSLC) Class 9 Mathematics.
- Number Systems — more Karnataka (SSLC) Class 9 Mathematics.
- Introduction to Euclid S Geometry — more Karnataka (SSLC) Class 9 Mathematics.
- All Karnataka (SSLC) Class 9 Mathematics chapters →