A game spinner is divided into four equal sectors coloured red
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A game spinner is divided into four equal sectors coloured red, blue, green and yellow. It was spun 250 times with the following observed frequencies:
Red – 90 times, Blue – 60 times, Green – 55 times, Yellow – 45 times.
(i) Calculate the empirical probability of the spinner landing on each colour.
(ii) Let the event E be “the spinner does not land on red.” Determine P(E) directly from the observed frequencies.
(iii) Without using the data for the other colours, find P(E) again by using the complement of the event “landing on red,” and verify that both answers are identical.
(iv) Prove that for any random experiment P(E)+P(E′)=1 where E′ is the complement of E.
(v) If the spinner is expected to be spun 800 times in a school carnival under similar conditions, estimate how many times the spinner will land on a colour other than red. Show detailed calculations.