Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

  • A
    Because the coin is circular.
  • B
    Because the outcomes are equally likely.
  • C
    Because it is a tradition.
  • D
    Because it is quick.

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One card is drawn from a well-shuffled deck of $52$ cards. Find the probability of getting:
$(i)$ a king of red colour
$(ii)$ a face card
$(iii)$ a red face card
$(iv)$ the jack of hearts
$(v)$ a spade
$(vi)$ the queen of diamonds

$A$ box contains $3$ blue,$2$ white,and $4$ red marbles. If a marble is drawn at random from the box,what is the probability that it will be
$(i)$ white?
$(ii)$ blue?
$(iii)$ red?

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$A$ game consists of tossing a one rupee coin $3$ times and noting its outcome each time. Hanif wins if all the tosses give the same result,i.e.,three heads or three tails,and loses otherwise. Calculate the probability that Hanif will lose the game.

Two dice,one blue and one grey,are thrown at the same time.
$(i)$ Complete the following table:
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Sum} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text{Prob.} & \frac{1}{36} & & & & & & \frac{5}{36} & & & & \frac{1}{36} \\ \hline \end{array}$
$(ii)$ $A$ 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 $\frac{1}{11}$.' Do you agree with this argument? Justify your answer.

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$A$ die is thrown twice. What is the probability that
$(i)$ $5$ will not come up either time?
$(ii)$ $5$ will come up at least once?

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