Exercise 32.2
Page no 32.31
Type 1
Question 1
Find the probability of getting the sum as a prime number when two dice are thrown together.
Question 2
A bag contains 20 balls numbered 1 to 20 . One ball is drawn at random. Find the probability that it is marked with a number which is a multiple of 5 or $7 .$
Question 3
A bag contains 3 green and 8 white balls. If one ball is drawn at random, find the chance that the ball drawn is green.
Question 4
A coin is tossed twice, what is the probability that at least one tail occurs ?
Question 5
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up in (i) 3 (ii) 12 .
Question 6
There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman ?
Question 7
A die is thrown, find the probability of following events :
(i) A prime number will appear,
(ii) A number greater than or equal to 3 will appear,
(iii) A number less than or equal to one will appear,
(iv) A number more than 6 will appear,
(v) A number less than 6 will appear.'
Question 8
A fair coin is tossed four times, and a person wins Re 1 for each head and loses Rs. $1.50$ for each tail that turns up.
From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.
Question 9
A group of researchers took a fair sample of 1972 children from the general population and found that there are 1000 boys and 972 girls, then what is the probability that a child born will be a girl?
Question 10
Two dice are thrown simultaneously. Find the probability of the sum of numbers coming up being a multiple of $4 .$
Question 11
If three coins are tossed simultaneously, find the probability of getting the following
(i) three head
(ii) two heads and one tail
(iii) same face head or tail on the three dice.
Question 12
What is the chance that a non-leap-year selected at random will have fifty-three Mondays?
Question 13
Find the probability that an ordinary year has 53 Sundays.
Question 14
What is the probability that a leap year has 53 Sundays and 53 Mondays ?
Question 15
In a single throw of three dice, find the probability of getting a total of 16 or $17 .$
Question 16
In a single throw of two dice, find
(i) $P$ (odd on first and 4 on second)
(ii) $P$ (a total $>8$ )
(iii) $P$ (a number $>4$ on each die)
Page no 32.32
Question 17
A box contains 6 blue marbles numbered 1 to 6 and 4 white marbles numbered 7 to 10 . Find the probability that a marble drawn is
(i) blue
(ii) blue and even numbered
(iii) odd numbered
(iv) white or odd numbered
Question 18
A die is thrown. Find :
(i) $P$ (a composite number)
(ii) $P$ (a number $\geq 3$ )
(iii) $P$ (a number $\leq 4$ )
(iv) $P$ (a number $>$ 6)
Question 19
A bag contains 3 red balls bearing the numbers 1,2 and 3 and 2 blue ball bearing the numbers 4 and 6 . A ball is drawn, its number is noted and the ball is replaced in the bag. Then another ball is drawn and its number is noter Find the probability of drawing.
(i) 1 on the first draw and 4 on the second
(ii) a number $<3$ on the first draw and 6 on the second draw
(iii) a total of 5
Question 20
Two dice are thrown. Find :
(i) the odds in favour of getting a sum of 5 .
(ii) the odds against getting a sum of 6 .
Question 21
What are the odds in favour of getting a spade if the card is drawn from a well-shuffled deck of cards? What are the odds in favour or getting a king?
Type 2
Question 22
A bag contains 3 red, 6 white and 7 black balls. Two balls are drawn at random, find the probability that both are black.
Question 23
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that :
(i) all the three balls are red,
(ii) all the three balls are blue.
Question 24
The letters of the word 'article' are arranged at random. Find the probability that the vowels may occupy the even places.
Question 25
What is the probability that four S's come consecutively in the world 'MISSISSIPPI'.
Question 26
Eleven books, consisting of 5 engineering books, 4 mathematics books and 2 physics books, are arranged in a shelf at random. What is the probability that the books of each kind are all together?
Question 27
A bag contains 4 white and 5 black balls two balls are drawn at random. Find the probability that one ball is white and the other is black.
Question 28
A bag contains 20 balls of which 6 are white, 4 are yellow, 5 are black and 5 are green. What is the probability that a ball drawn at random is either white or black or green ?
Question 29
In a throw of two dice, find the chance of getting a total of 3 or 6 or 12 .
Question 30
A bag contain 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that
(i) all the three balls are blue balls.
(ii) all the balls are of different colours.
Page no 32.33
Question 31
A word has 7 letters, consisting of 4 consonants and 3 vowels. Three letters are chosen at random. What is the probability that more than one vowel is selected?
Question 32
A box contains 100 bulbs out of which 20 are defective. 10 bulbs are selected at random from the box. Find the probability of selecting.
(i) only non-defective bulbs
(ii) only defective bulbs
(iii) no defective bulb.
Question 33
A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black ?
Question 34
An urn contains 9 red, 7 white and 4 black balls. One ball is drawn at random. What is the probability that it is red or black?
Question 35
In a lucky draw, a person selects six numbers at random from 1 to 20 and if all of these numbers match with six winning numbers fixed by the committee, the person wins the prize. What is the probability of his winning the prize in the draw ?
Question 36
In shuffling a pack of cards, four are accidently dropped, find the chance that the dropped cards should be one from each suit ?
Question 37
Four cards are drawn at a time from a pack of 52 playing cards. Find the probability of getting all the 4 cards of the same suit.
Question 38
Five persons entered a lift on the ground floor of an 8-floor house. Suppose that each of them independently and with equal probability can alight from the lift at any floor beginning with the first. Find the probability of all five persons leaving at different floors.
Question 39
Three tickets are drawn at random out of 21 tickets marked with numbers 1 to 21. Find the probability that the three numbers are in A.P.
Type 2
Question 40
A letter is chosen at random from the word 'ASSASSINATION". Find the probability that letter is (i) a vowel (ii) a consonant.
Question 41
A card is selected from a pack of 52 cards.
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) a black card.
Question 42
If $P(A)=\frac{1}{3}, P(B)=\frac{1}{2}, P(A \cap B)=\frac{1}{4}$ then find $P\left(A^{\prime}\right), P\left(B^{\prime}\right)$ and $P\left(A^{\prime} \cup B^{\prime}\right)$
Question 43
If two dice are thrown, what is the probability that unequal numbers will come up on them ?
Question 44
Four coins are tossed together. What is the probability that head will appear on at least one of the four?
Question 45
Three letters, to each of which corresponds on envelope, are placed in the envelops at random. Find the probability that all the letters are not placed in the right envelops.
Question 46
In a single throw of three dice, determine the probability of getting a total of at least 5 .
Page no 32.34
Question 47
What is the probability that in a group of an persons, at least two of them will have the same birthday ?
Question 48
A box contains 15 electric bulbs, out of which 2 are defective Two bulbs are chosen at random from this box. What is the probability that at least one is defective ?
Question 49
If the probability of occurrence of an event is $\frac{2}{13}$, find the odds against the event.
Question 50
4 boys and 3 girls are seated in a row, find the odds in favour and odds against all the girls sitting together.
Question 51
In the throw of two dice, what are the odds in favour of the sum of the numbers coming up being at least 10 ?
Question 52
What are the odds in favour of throwing at least 7 in a single throw with two dice?
Question 53
Find the odds in favour and odds against drawing 2 kings from a pack of 52 playing cards .
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