Solution:
Concept
Probability = No. of possible outcomes / No. of sample space
No. of sample space (Total numbers in the set or under examination) =12
We have to list the prime numbers of the set p and count them to get the No. of possible outcomes
A prime is a number that is greater than 1 and divisible only by itself and 1 (e.g. 2,3,5,7,11,... )
Note: 1 is not a prime number
⇒ the prime numbers from the set p are {2,3,5,7,11}
The total possible prime numbers is 5 (when you count the list of prime numbers above, you are to get 5)
⇒ The probability of selecting a prime number =5∕12
What will the probability of selecting i)an even number ii) old number?
i) Probability of selecting an even number
An even number is a number divisible by 2
Hence the even numbers from set p are {2,4,6,8,10,12} which when you count you will get 6
⇒ The probability of selecting an even number =6∕12=1∕2
ii) Probability of selecting an odd number
Odd numbers are whole numbers that cannot be divided exactly into pairs. Odd numbers, when divided by 2, leave a remainder of 1.
Hence the odd numbers from set p are {1,3,5,7,9,11} which when you count you will get 6
⇒ The probability of selecting an odd number =6∕12=1∕2
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