Question

People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease.1 The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia.Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.Round your answer to three decimal places.

Answer 1

0.1833

Explanation:

Given:

% of people with fibromyalgia = 2%

Probability of having a restless leg syndrome for people with fibromyalgia = 0.33

Probability of having a restless leg syndrome for people without fibromyalgia = 0.03

Take F as event of having fibromyalgia

Take R as event of having restless leg

Required:

Find the probability that a person with restless leg syndrome has fibromyalgia.

To find the probability that a person with restless leg syndrome has fibromyalgia, we have: P(F/R)

`P(F/R) = (P(F n R))/(P(R))`

`P(F/R) =(P(R/F) * P(F))/(P(R/F) * P(F) + P(R/F^c) * P(F^c))`

Where,

P(R/F) = 0.33

P(F) = 2% = 0.02

P(R/F') = 0.03

P(F') = 1 - 0.02 = 0.98

Therefore,

`P(F/R) = (0.33 * 0.02)/(0.33*0.02 + 0.03*0.98)`

= 0.1833

Probability a person with restless leg syndrome has fibromyalgia = 0.1833

Tree diagram is attached