Download Simple Idea of Probability

Simple Idea of Probability
1.
Two dice are thrown. Find the probability that
(a) the sum is 12.
(b) the sum is 6.
1 1 1
P(the sum is 12)=  
6 6 36
5 1 5
P(the sum is 6)=  
6 6 36
(c) the product is 6.
(d) the sum is 2 or 12.
2 2 1
P(the product is 6)=  
6 6 9
1 1 1 1 1
P(the sum is 2 or 12)=    
6 6 6 6 18
(e) at least one die is 5.
(f) the sum is less than 5.
1 6 6 1 1 11
P(at least one die is 5)=    

6 6 6 6 36 36
1 3 1 2 1 1 1
P(the sum is less than 5)=      
6 6 6 6 6 6 6
 The outcome (5, 5) occurs twice.
 The number of favorable outcomes is 11
2.
A die is thrown twice. What is the probability of getting
(a) the first being 5 and the second less than 5?
(b) the first being less than the second?
P(the first being 5 and the second less than 5)
1 4 1
  
6 6 9
3.
P(the first being less than the second)
1 5 1 4 1 3 1 2 1 1 5
          
6 6 6 6 6 6 6 6 6 6 12
John chooses at random a number from 1, 2, 3 and May chooses at random a letter from A, B, C, D and E.
What is the probability that the result is ‘3’ and ‘A’ ?
1 1 1
P(the result is ‘3’ and ‘A’)=  
3 5 15
4.
24*6 is a number of 4 digits and * represents any digit from 0 to 9. What is the probability that the number
is divisible
(a) by 2 ?
(b) by 3 ?
4 2
P(the number is divisible by 2)=1
P(the number is divisible by 3)= 
10 5
5.
A bag contains 2 red balls and 2 white balls. 2 balls are taken out successively without replacement. Find the
probability that both balls are red.
2 1 1
P(both balls are red)=  
4 3 6
6.
The age distribution of a class is given as shown. If a student is selected at random, find the probability that
Age
13
14
15
16
No. of students
12
10
15
3
(a) his age is 14 or 15.
P(his age is 14 or 15)=
(b) he is younger than 15.
10 15 25 51



40 40 40 8
P(he is younger than 15)=
12  10 22 11


40
40 20
7.
A bag contains ten numbered balls: 1, 2, 3, 3, 4, 4, 4, 5, 6, and 8. A ball is chosen at random from the bag.
Find the probability of getting
(a) an even number.
(b) a number which is divisible by 4 (b) a prime number.
6 3
4 2
4 2
P(an even number)= 
P(divisible by 4)= 
P(a prime number)= 
10 5
10 5
10 5
8.
An urn contains 100 balls of which 20 are white, 25 are green, 15 are black, 10 are blue and the rest are red.
One ball is selected at random. What is the probability that it is
(a) green?
(b) blue or red?
(c) not white?
10
30 2
20 4
25 1
P(blue or red)=
P(not white)= 1 



P(green)=

100 100 5
100 5
100 4
(d) orange?
P(orange)= 0
9.
(e) neither black nor white?
P(neither black nor white)
15
20 13
=1 


100 100 20
A card is selected from a pack of 52 cards. What is the probability of getting
(a) a picture card?
(b) a King or a heart?
3 4 3
4 13 1 16 4
P(a picture card)=
P(a King or a heart)= 




52
13
52 52 52 52 13
10. In a family of 3 children, find the probability that there are
(a) 3 boys.
(b) 2 boys and 1 girl.
1 1 1 1
P(3 boys)=   
1 1 1 3
2 2 2 8
P(2 boys and 1 girl)= 3    
 2 2 2 8
(c) no boys.
1 1 1 1
P(no boys)=   
2 2 2 8
(d) at least one boy.
1 1 1 3
P(at least one boy)= 3    
 2 2 2 8
11. A coin is tossed and a die is thrown. Find the probability that
(a) a head and a ‘4’ appear.
(b) a head and an odd number appear.
1 1 1
1 3 1
P(a head and a ‘4’)=  
P(a head and an odd number)=  
2 6 12
2 6 4
(c) a tail and a number less than 6 appear.
1 5 5
P(a tail and a number less than 6)=  
2 6 12
12. One man and one woman are to be selected at random from a group of 3 men and 5 women. If there is a
couple among these people, find the probability that
(a) both of them are chosen.
(b) neither of them are chosen.
1 1 1
2 4 8
P(both of them are chosen)=  
P(neither of them are chosen)=  
3 5 15
3 5 15
(c) one of them is chosen.
1 4 1 2 2
P(one of them is chosen)=    
3 5 5 3 5
13. In a family of three children, what is the 14. In rolling two dice, what is the probability of
probability that at least two of the children are
getting a double?
girls?
1 1 1
P(getting a double)= 6   
1 1 1
P(at least two girls)= 2   
6 6 6
 2 2 2
15. The following is torn from a page of a telephone 16. Refer to Question 15, if it is known that the
guide.
missing digits are two consecutive numbers, what
Mr. C. Chan 2543 1234
is the probability of getting the correct telephone
Mr. C. Kwan 2888 8888
number?
1 1
Mr. J. Lee 2777 77XX
P(correct telephone number)= 1  
9 9
The last two digits are missing. What is the
probability of getting Mr. Lee’s telephone number
correctly?
1 1
1
P(correct telephone number)=  
10 10 100
17. A bag contains 6 red balls and some white balls. If 18. In throwing 3 coins, what is the probability of
getting 3 heads or 3 tails?
5
the probability of getting a white ball is , find
1 1 1
8
P(3 heads or 3 tails)=  
8 8 4
the number of white balls in the bag.
Let n be the number of white balls in the bag.
P(a white ball)=
5
n

8 n6
8n  5n  30
n  10
 The number of white balls in the bag is 10.
19. The following table shows the number of bad 20. In MARK SIX, 6 numbers are drawn from 49
apples in some boxes of apples.
different numbers. What is the probability of
getting the first prize?
No. of bad apples
0
1
2
3
4
P(getting the first prize)
No. of boxes
12 22
8
6
2
A merchant will get a loss if a box contains more
than 2 bad apples. What is the probability that he
will get loss?
P(he will get loss)=
62 8

 0.16
50
50
6 5
4
3 2 1
    
49 48 47 46 45 44
720
1


10068347520 13983816

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