Question

24. Cards are marked with numbers from 10 to
50 and well shuffled. One card is drawn at
random. What is the probability that it is a
number
(i) divisible by 5 (ii) a perfect square
(iii) a multiple of 3 and 4
(iv) with one of the digits 5​

Answer 1

Total number of cards (from 10 to 50) = 40

Total number of possible outcomes = Total number of cards = 40

i.) divisible by 5

Numbers of cards which are divisible by 5 are 9 (i.e. 10, 15, 20, 25, 30, 35, 40, 45 and 50)

Number of favourable outcomes = Numbers of cards which are divisible by 5 = 9

$Probability\:\:(divisible\:\:by\:\:5) =\frac{Number\:\:of\:\:favourable\:\:outcomes}{Total\:\:number\:\:of\:\:possible\:\:outcomes}\\ \\=\frac{9}{50}$

ii.) a perfect square

Numbers of cards which are a perfect square are 4 (i.e. 16, 25, 36, and 49)

Number of favourable outcomes = Numbers of cards which are a perfect square = 4

$Probability\:\:(a\:\:perfect\:\:square) =\frac{Number\:\:of\:\:favourable\:\:outcomes}{Total\:\:number\:\:of\:\:possible\:\:outcomes}\\ \\=\frac{4}{50} \\ \\ =\frac{2}{25}$

iii.) a multiple of 3 and 4

Numbers of cards which are a multiple of 3 and 4 are 19(i.e. 12, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 33, 36, 39, 40, 42, 44, 45 and 48)

Number of favourable outcomes = Numbers of cards which are a multiple of 3 and 4 = 19

$Probability\:\:(a\:\:multiple\:\:of\:\:3\:\:and\:\:4) =\frac{Number\:\:of\:\:favourable\:\:outcomes}{Total\:\:number\:\:of\:\:possible\:\:outcomes}\\ \\ =\frac{19}{50}$

iv.) with one of the digits 5

Numbers of cards with one of the digits 5 are 5 (i.e. 15, 25, 35, 45 and 50)

Number of favourable outcomes = with one of the digits 5 = 5$Probability\:\:(with\:\:one\:\:of\:\:the\:\:digits\:\:5) =\frac{Number\:\:of\:\:favourable\:\:outcomes}{Total\:\:number\:\:of\:\:possible\:\:outcomes}\\ \\ =\frac{5}{50} \\ \\=\frac{1}{10}$

Answer 2

Answer:

Step-by-step explanation:

(i) no divisible by 5=10,15,20,25,30,35,40,45,50

No are: 10,Total=50-10+1=41

P =10/41

(ii) 12,24,36,48

P=4/41

(III)

15,25,35,45,50

P=5/41