Question

11 You randomly choose a number from 1 to 10. Find P(even or less than 5).

Answer 1

You randomly choose a number from 1 to 10

We are asked to find the probability P(even or less than 5)

There are a total of 10 possible numbers

$1,2,3,4,5,6,7,8,9,10$

How many of them are even?

$even=2,4,6,8,10$

There are 5 even numbers.

So, the probability of getting an even number is

$P(even)=\frac{5}{10}=\frac{1}{2}=0.5$

How many of them are less than 5?

$less\: than\: 5=1,2,3,4$

There are 4 numbers less than 5.

So, the probability of getting a number less than 5 is

$P(less\: than\: 5)=\frac{4}{10}=\frac{2}{5}=0.4$

Finally, we need to add these probabilities to find the combined probability (or means to add)

$\begin{gathered} P(even\: or\: less\: than\: 5)=P(even)+P(less\: than\: 5) \\ P(even\: or\: less\: than\: 5)=0.5+0.4 \\ P(even\: or\: less\: than\: 5)=0.90 \end{gathered}$

Therefore, the probability P(even or less than 5) is 0.90