BECE Mathematics 2020 Paper

ConceptProbability = No. of possible outcomes / No. of sample spaceNo. 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 outcomesA prime is a number that is greater than 1 and divisible only by itself and 1 (e.g. $2,3,5,7,11,\dots$ ) Note: 1 is not a prime number$\Rightarrow$ 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)$\Rightarrow$ The probability of selecting a prime number $=\frac{5}{12}$What will the probability of selecting i)an even number ii) old number?i) Probability of selecting an even numberAn 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$\Rightarrow$ The probability of selecting an even number $=\frac{6}{12}=\frac{1}{2}$ii) Probability of selecting an odd numberOdd 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$\Rightarrow$ The probability of selecting an odd number $=\frac{6}{12}=\frac{1}{2}$