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A Man has four pairs of shoes three suits and four shirts if he picks a pair of shoes, a suit, and a shirt at random, what is the probability that he picks his favorite shoes, suit, and shirt? Enter the probability as a fraction

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SOLUTION

The man has 4 pairs of shoes

3 suits and

4 shirts

Probability is given as

[tex]\text{Probability = }\frac{\exp ected\text{ outcome }}{\text{total outcome }}[/tex]

If he is to pick his favorite pair of shoes, suit and shirts, it means he will pick 1 pair of shoe, 1 suit and 1 shirt.

Then the probability of picking

His favorite pair of shoes becomes

[tex]\frac{1}{4}[/tex]

Then the probability of picking

His favorite suit becomes

[tex]\frac{1}{3}[/tex]

And Then the probability of picking

His favorite shirt becomes

[tex]\frac{1}{4}[/tex]

Hence the required probability is

[tex]\begin{gathered} \frac{1}{4}\times\frac{1}{3}\times\frac{1}{4} \\ =\frac{1}{48} \end{gathered}[/tex]

Hence the answer is

[tex]\frac{1}{48}[/tex]

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