Question

A psychology test has personality questions numbered 1,2,3, intelligence questions numbered 1,2,3,4, and attitude questions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?Provide the final answer as a simplified fraction.

Answer 1

Given:

Personality question = 1,2,3

Intelligence question = 1,2,3,4

Attitude question = 1,2

Find-: what is the probability that the question is an intelligence question OR has an odd number

Sol:

The total number of questions is:

3 Personality, 4 intelligence, and 2 attitudes so the total number of questions is:

`\begin{gathered} =3+4+2 \\ \\ =9 \end{gathered}`

The odd numbers are:

`\begin{gathered} =1,1,1,3,3 \\ \\ \text{ Total 5 questions.} \end{gathered}`

Probability is :

`P=\frac{\text{ Favorable outcome }}{\text{ Total outcome}}`

The probability of an odd number is:

`P=(5)/(9)`

The probability of intelligence question of even number is:

`P=(2)/(9)`

So required probability is:

`\begin{gathered} =(5)/(9)+(2)/(9) \\ \\ =(7)/(9) \end{gathered}`

Probability is 7/9.