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Question

In a lottery of 50 tickets numbered 1to 50 one ticket is drawn. Find the probability that the drawn ticket bears a prime number.


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Solution

Step 1: Use formula of probability

PA=number of outcome favourable to Atotal number of possible outcome

or

PA=nAnS

where,

  • PAis probability of an event'A'
  • nAis the favorable outcome of the event 'A'

nSis total number of possible outcome in a sample space

Step 2: The probability of getting a prime number on ticket

Let, A be the event of “getting a prime number on ticket ”

Then, Total number of tickets is 50 .

S is a sample space of all the possible outcomes which is 50tickets.

Thus, total number of possible outcome in a sample space is nS=50

Number of prime numbers are

2,3,5,7,11,13,17,19,23,29,31,37,41,43and 47.

Thus, the favorable outcome of the event 'A' is nA=15

The probability of getting a prime number on ticket PAis,

PA=number of tickets with prime numbertotal number of tickets=nAnS

Substitute the values on the formula,

PA=1550=310

Hence, the probability of getting a prime number on ticket is 310.


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