Q. 1 A3.9( 7 Votes )
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.
(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.
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Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is
(i) an odd number
(ii) a perfect square number
(iii) divisible by 5
(iv) a prime number less than 20RD Sharma - Mathematics
The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen
(iii) clubs.RD Sharma - Mathematics
Two dice, one blue and one grey, are thrown at the same time. Complete the following table:
From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability . Do you agree with this argument?RD Sharma - Mathematics
Fill in the blanks:
(i) Probability of a sure event is ………. .
(ii) Probability of an impossible event is ………….. .
(iii) The probability of an event (other than sure and impossible event) lies between ……….. .
(iv) Every elementary event associated to a random experiment has ………. Probability.
(v) Probability of an event A+ Probability of event ‘not A’ = ………….. .
(vi) Sum of the probabilities of each outcome in an experiment is …………. .RD Sharma - Mathematics
Cards marked with numbers 13, 14, 15, …, 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is
(i) divisible by 5
(ii) a number is a perfect squareRD Sharma - Mathematics
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above you prefer more.RD Sharma - Mathematics
A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue cardRD Sharma - Mathematics
A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.RD Sharma - Mathematics
Examine each of the following statements and comment:
(i) If two coins are tossed at the same time, there are 3 possible outcomes – two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is 1/3.
(ii) If a die is thrown once, there are two possible outcomes – an odd number or an even number. Therefore, the probability of obtaining an odd number is � and the probability of obtaining an even number is 1/2.RD Sharma - Mathematics