Q1.
Two dice are rolled. is the event that the sum of the numbers shown on the two
dice is and is the event that at least one of the dice shows up a . Are the two
events (i) mutually exclusive. (ii) exhaustive ? Give reasons.
Q2.
cards are numbered from
. One card is drawn at random. What is the
probability that the number on the card drawn is :
(i)a prime number.
(ii) a multiple of .
(iii) not divisible by .
Q3.
Two dice are thrown simultaneously. Find the probability of getting:
(i)a doublet (ii) a prime number as the sum and (iii)an even number as the sum.
Q4.
From a well shuffled deck of
cards, a card is drawn at random. Find the
probability that the card drawn is:
(i)red and a king (ii) either red or a king.
Q5.
Two coins are tossed once, find the probability of getting:
(i) heads (ii) no heads (iii) at least one head (iv)
head and
tail.
Q6.
If the odds against the occurrence of an event be
occurrence of the event.
Q7.
In a single throw of two dice, determine the probability of not getting the same
number on the two dice.
Q8.
If there are two children in the family, find the probability that there is at least one
boy in the family.
Q9.
Which of the following cannot be the probability of occurrence of an event?
(i) (ii)
Q10.
(iii)
, find the probability of the
(iv)
Check whether the following probabilities
(i)
are consistently defined
(ii)
Give reasons.
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Q11.
In a single throw of two dice, find the probability that neither a doublet nor a total of
appears.
Q12.
Two cards are drawn at random from a well shuffled pack of
probability that either both are red or both are kings?
Q13.
The probabilities of the occurrence of two events
are
respectively. The probabilities of their simultaneous occurrence is
probability that neither
nor
occurs.
Q14.
The probability that Hemant passes in English is
cards. What is the
. Find the
and the probability that he passes
in Hindi is . If the probability of his passing in both the subjects is , find the
probability that he will pass in at least one of these subjects.
Q15.
A bag contains red and
white balls. One ball is drawn at random. Find the
probability that the ball drawn is red.
Q16.
Tickets numbered from
are mixed up together and then a ticket is withdrawn
at random. Find the probability that the ticket has a number which is a multiple of
.
Q17.
A box contains
red marbles,
blue marbles and
green marbles. Five marbles
are drawn from the box. What is the probability that all will be blue ?
Q18.
cards are drawn at a time from a well shuffled pack of
probability of getting all the four cards of the same suit.
Q19.
If
cards. Find the
is the probability that an event will happen, what is the probability that it will
not happen ?
Q20.
If a letter is chosen at random from the English alphabets, find the probability that
the letter chosen is (i) a vowel (ii) a consonant.
Answers
A1.
are neither mutually exclusive nor exhaustive events. Because
and
.
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A2.
(i) (ii)
A3.
(i) (ii)
A4.
(i)
A5.
(i) (ii)
(iii)
.
(iii)
(ii)
(iii)
(iv)
A6.
A7.
A8.
A9.
(ii) and (iv)
A10.
(i) No, because
should be
(ii) Yes
A11.
A12.
A13.
A14.
A15.
A16.
A17.
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A18.
A19.
A20.
(i)
(ii)
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