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

Answer:

i) The probability that the number on the ticket is even is $\mathbf{\frac{1}{2}}$

ii) the probability that the number on the ticket is a number less than 16 is $\mathbf{\frac{6}{23}}$

iii) The probability that the number on the ticket is a perfect square is $\mathbf{\frac{5}{46} }$

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

Step-by-step 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: $Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}$

Total number of outcomes = 46

Number of favourable outcomes = 23

Putting values and finding probability

$Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{23}{46}\\Probability=\frac{1}{2}$

So, the probability that the number on the ticket is an even number is $\mathbf{\frac{1}{2}}$

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: $Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}$

Total number of outcomes = 46

Number of favourable outcomes = 12

Putting values and finding probability

$Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{12}{46}\\Probability=\frac{6}{23}$

So, the probability that the number on the ticket is a number less than 16 is $\mathbf{\frac{6}{23}}$

iii) a perfect square

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

Total number of favourable outcomes = 5

So, the formula used is: $Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}$

Total number of outcomes = 46

Number of favourable outcomes = 5

Putting values and finding probability

$Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{5}{46}$

So, the probability that the number on the ticket is a perfect square is $\mathbf{\frac{5}{46} }$

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: $Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}$

Total number of outcomes = 46

Number of favourable outcomes = 8

Putting values and finding probability

$Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{8}{46}\\Probability=\frac{4}{23}$

So, the probability that the number on the ticket is a prime number less than 30 is $\mathbf{\frac{4}{23} }$