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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.

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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.

User Victor Augusto
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