Question

Tickets numbered 4, 5, 6......48, 49 are placed in a box and mixed thoroughly. One ticket is drawn from the box. Find the probability that the number on the ticket is:

(i) an even number (ii) A number less than 16
(iii) a perfect square (iv) a prime number less than 30.

Answer 1

i) The probability that the number on the ticket is even is
`\mathbf{(1)/(2)}`

ii) the probability that the number on the ticket is a number less than 16 is
`\mathbf{(6)/(23)}`

iii) The probability that the number on the ticket is a perfect square is
`\mathbf{(5)/(46) }`

iv) the probability that the number on the ticket is a prime number less than 30 is
`\mathbf{(4)/(23) }`

Explanation:

Tickets numbers are: 4, 5, 6......48, 49

So, total tickets in box = 46

We need to find probability that the number on the ticket is:

i) an even number.

Even number in tickets are: 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48

Total number of favourable outcomes = 23

So, the formula used is:
`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)`

Total number of outcomes = 46

Number of favourable outcomes = 23

Putting values and finding probability

`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)\\Probability=(23)/(46)\\Probability=(1)/(2)`

So, the probability that the number on the ticket is an even number is
`\mathbf{(1)/(2)}`

ii) A number less than 16

Even number in tickets are: 4,5,6,7,8,9,10,11,12,13,14,15

Total number of favourable outcomes = 12

So, the formula used is:
`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)`

Total number of outcomes = 46

Number of favourable outcomes = 12

Putting values and finding probability

`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)\\Probability=(12)/(46)\\Probability=(6)/(23)`

So, the probability that the number on the ticket is a number less than 16 is
`\mathbf{(6)/(23)}`

iii) a perfect square

Perfect squares are: 4,9,16,25,36

Total number of favourable outcomes = 5

So, the formula used is:
`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)`

Total number of outcomes = 46

Number of favourable outcomes = 5

Putting values and finding probability

`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)\\Probability=(5)/(46)`

So, the probability that the number on the ticket is a perfect square is
`\mathbf{(5)/(46) }`

iv) a prime number less than 30.

Prime numbers less than 30 are: 5,7,11,13,17,19,23,29

Total number of favourable outcomes = 8

So, the formula used is:
`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)`

Total number of outcomes = 46

Number of favourable outcomes = 8

Putting values and finding probability

`Probability=(Number\:of\:favourable\:outcomes)/(Total\:number\:of\:outcomes)\\Probability=(8)/(46)\\Probability=(4)/(23)`

So, the probability that the number on the ticket is a prime number less than 30 is
`\mathbf{(4)/(23) }`