Question

Which of the following have ‘equally likely’ outcomes? Explain. (i) A player calls for a head in a toss of a coin. The coin shows up either heads or tails. (ii) Mr Sharma has one child. The child is either a boy or a girl. (iii) An attempt was made to answer a true-false question. The answer is correct or incorrect. (iv) A batsman plays and misses a ball. The ball either hits the wickets or misses them. Select the correct answer from above options

Answer 1

(i) Equally likely outcome: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. In a toss of a coin occurrence of head or tail have equal probabilities. Thus it has an equally likely outcome of head and tail (ii) Equally likely outcome: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. Birth of a boy or a girl has an equal probability. Now Mr Sharma has one child. The child is a boy, or a girl has an equal probability and hence it is an equally likely outcome. (iii) Equally likely outcome: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. For a true false question there are only two probabilities: True or False. Now the sample space of the attempt contains two possibilities True or False. There can be only one correct answer for the event. Hence there is equal possibilities of answer being correct or incorrect and therefore it is an equally likely outcome. (iv) Equally likely outcome: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. A player plays a ball and misses it. Now there are many possibilities of the path took bby ball after being missed by batsman. Hence occurrence of ball hitting wicket is not an equally likely outcome with missing. As it may go to wicketkeeper or it may go pass wicket keeper. Thus there are many possibilities for the event.