A bag contains 200 balls that are either red or blue and either dull or shiny. T

Question

A bag contains 200 balls that are either red or blue and either dull or shiny. There are 55 shiny red balls, 91 shiny balls, and 79 red balls. If a ball is chosen at random, what is the probability that it is either a shiny ball or a red ball? What is the probability that it is a dull blue ball? In a study of patients arriving at a hospital emergency room, the gender of the patients is considered, together with whether the patients are younger or older than 30 years of age, and whether or not the patients are admitted to the hospital. It is found that 45% of the patients are male, 30% of the patients are younger than 30 years of age, 15% of the patients are females older than 30 years of age who are admitted to the hospital, and 21 % of the patients are females younger than 30 years of age. What proportion of the patients are females older than 30 years of age who are not admitted to the hospital?

Explanation / Answer

1.3.12

91 are shiny, and 55 are shiny red.

Hence, 91 - 55 = 36 are shiny blue.

79 are red. Hence, 200-79 = 121 are blue.

Hence, 121-36 = 85 are dull blue.

a)

Thus,

P(shiny or red) = P(shiny) + P(red) - P(shiny and red)

= 91/200 + 79/200 - 55/200

= 0.575 [ANSWER]

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b)

As 85 are dull blue,

P(dull and blue) = 85/200 = 0.425 [ANSWER]

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