Question

Can you help me understand the steps to number 21 I think I got it wrong

Answer 1

The probability of an event is determined a follows;

`P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}`

We shall begin with the probability of selecting an even number as shown below;

`\begin{gathered} P\lbrack\text{even\rbrack}=(6)/(12) \\ P\lbrack\text{even\rbrack}=(1)/(2) \end{gathered}`

Next we shall calculate the probability of selecting a number less than 5 as shown below;

`\begin{gathered} P\lbrack\text{less than 5\rbrack=}(4)/(12) \\ P\lbrack\text{less than 5\rbrack=}(1)/(3) \end{gathered}`

The probability of event A OR event B occuring is calculated a follows;

`\begin{gathered} P\lbrack A\rbrack\text{ OR P\lbrack{}B\rbrack=P\lbrack{}A\rbrack+P\lbrack{}B\rbrack} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}(1)/(2)+(1)/(3) \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}(3+2)/(6) \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}(5)/(6) \end{gathered}`

The probability of selecting an even number or a number less than 5 is therefore

`(5)/(6)`

The correct answer is option A