Question

A box has cards with numbers 21, 22, 23…….40. A card is chosen at
random. What is the probability that the card chosen at random is
i) A prime number
ii) Sum of the digits is a multiple of 3
iii) Divisible by 4 or 5.

Answer 1

Given:

The possible outcomes are:

21, 22, 23, ……., 40

Total number of possible outcomes = 20

Solution:

i) A prime number

The prime numbers between 21 to 40:

23, 29, 31 and 37

Number of favourable outcomes = 4

∴ Probability(getting a prime number) = $\dfrac{Number of favourable outcomes}{Total number of possible outcomes}$

= $\dfrac{4}{20}$ or, $\dfrac{1}{5}$

ii) Sum of the digits is a multiple of 3

The sum of the digits is a multiple of 3 are:

21, 24, 27, 30, 33, 36 and 39

The number of favourable outcomes = 7

∴ Probability(getting a sum of digits is multiple of 3) = $\dfrac{Number of favourable outcomes}{Total number of possible outcomes}$

= $\dfrac{7}{20}$

iii) Divisible by 4 or 5

The numbers are divisible by 4 or 5:

24, 25,28, 30, 32, 35, 36 and 40

The number of favourable outcomes = 8

∴ Probability(getting a number divisible by 4 or 5) = $\dfrac{Number of favourable outcomes}{Total number of possible outcomes}$

= $\dfrac{8}{20}$ = $\dfrac{2}{5}$

Answer 2

Given : A box has cards with numbers 21, 22, 23  ,  40.  

A card is chosen at  random.

To Find :What is the probability that the card chosen is

i) A prime number

ii) Sum of the digits is a multiple of 3

iii) Divisible by 4 or 5.

Solution:

A box has cards with numbers 21, 22, 23 ,    40.  

=> n(S) = 20

card chosen is   A  = prime number

23 , 29 , 31 , 37  

n(A) = 4

Probability that the card chosen is  prime number  = n(A)/n(S) = 4/20 = 1/5

B =  Sum of the digits is a multiple of 3

Hence number is multiple of 3

21  , 24 , 27 , 30 , 33 , 36 , 39

n(B) = 7

Probability that the card chosen has  sum of the digits as a multiple of 3 = n(B)/n(S) =7/20

Divisible by 4 or 5.

= Divisible by 4 + Divisible by 5 - Divisible by 20

Divisible by 4 = 24 , 28 ,32 , 36 , 40

Divisible by 5 = 25 , 30 , 35 , 40

Divisible by 20 =  40

5 + 4 - 1 = 8

Probability that the card chosen Divisible by 4 or 5. = 8/20  = 2/5

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