Two different science clubs carried out experiments and recorded the following…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
Two different science clubs carried out experiments and recorded the following results:
Club X (Experiment 1): An unbiased die was rolled 90 times. The face ‘6’ appeared 21 times.
Club X (Experiment 2): The same die was rolled another 60 times. The face ‘6’ appeared 18 times.
Club Y (Experiment 3): A different die was rolled 40 times. The face ‘6’ appeared 9 times.
Club Y (Experiment 4): A coin was tossed 80 times and heads appeared 47 times.
Answer the questions below, showing all steps in your reasoning.
(i) For each of the four experiments, compute the empirical probability of the stated event. Express every probability both as a simplified fraction and as a decimal correct to three decimal places.
(ii) Convert all the probabilities obtained in part (i) to percentages and arrange the four events in ascending order of likelihood. Identify any pair of events that are equally likely.
(iii) For Club X, combine the results of its two experiments and find the overall empirical probability of obtaining a ‘6’. Compare this combined probability with the individual probabilities listed earlier and comment on any change in likelihood.
(iv) Using the complement rule, find the empirical probability of NOT getting heads in Experiment 4. Explain how this complements your ranking in part (ii).