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There are twelve shirts in your closet, five blue and seven green. four of the blue shirts and one of the green shirts fit well. the others are too big. you randomly select a shirt to wear. it is blue or is too big. find the probability of this occurring.

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There are 5 blue shirts and only one is big, so the probability would be 1/12. The percentage would be approximately 8%

Answer:

Answer is : [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Total number of shirts : 12

  • Blue shirts : 5  (fit blue shirts : 4 , too big blue shirts : 1)
  • Green shirts : 7 (fit green shirts : 1, too big green shirts : 6)  

We need to find the probability of randomly select a shirt which is blue or too big.

Here two conditions are blue or too big. Means we have to add the probability of both the conditions because of  OR.

OR : one condition should satisfy at a time or the other one or both.(all conditions probability will add)

AND : all conditions should satisfy at a time.( all conditions probability will multiply)

  • Probability of being a shirt blue = [tex]\frac{possible outcome}{total outcome}[/tex] = [tex]\frac{5}{12}[/tex]
  • Probability of being a shirt too big = [tex]\frac{x}{y} \frac{probable outcome}{total outcome}[/tex] = [tex]\frac{6}{12}[/tex]

∵ 6 = (7-1), because one too big  shirt already counted in blue shirts probability.

∴ Probability of being a shirt blue or too big is : [tex]\frac{5}{12}[/tex] + [tex]\frac{6}{12}[/tex] = [tex]\frac{11}{12}[/tex]

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