Probability Problems
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This document provides a tutorial on probability problems with examples and solutions. It contains two questions: 1) A coin is tossed 1000 times with 499 heads and 501 tails. The empirical probability of heads is 0.499 and tails is 0.501. The sum of the two probabilities equals 1. 2) In a cricket match, a batswoman hits a boundary 6 times out of 30 balls. The probability that she did not hit a boundary is calculated as 24/30 = 4/5. The document explains how to calculate empirical probabilities from sample data and find the probability of complementary events. It provides the full worked out solutions and explanations.
Probability Problems
- 2. Quiz Question 1: A coin is tossed 1000 times; we get 499 times head and 501 times 1) What is the empirical probability of getting head ? 2) What is the empirical probability of getting tail? 3) Does the sum of above two probability equals 1?
- 3. Solution Total number of trials =1000 No of trails which head came =499 So No of trails where tail came=1000-499=501 a) Now Empirical probability of getting head=(No of trails which heads came)/(Total Number of trials) empirical probability of getting head=499/1000 So empirical or experimental probability of getting head P(H) is calculated as =.499
- 4. Solution b) empirical probability of getting tail =(No of trails which tails came)/(Total Number of trials) Sp empirical probability of getting head=501/1000 So empirical or experimental probability of getting head P(T) is calculated as =.501 c) Now P(H) +P(T)= .499+.501=1
- 5. Question-2 In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Solution: Let P is the event of hitting the boundary n(P)=6 Let Q be the event of not hitting the boundary n(Q)= 30- n(P)=24 Probability of not hitting the boundary= n(Q)/30= 24/30=4/5
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