Question

Diseases I and II are prevalent among people in a certain population. It is assumed

that 10% of the population will contract disease I sometimes during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases. Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime. Also, Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime.

Answer 1

Answer: a) 0.22 b) 0.1363

Explanation:

People who contract disease I are= 10%

People who contract disease II are= 15%

People who contract both diseases are= 3%

a)

People who contract has at least one disease needs to be found out so it is given as

P(D1 or D2)= P(D1) + P(D2) - P(D1 and D2)

P(D1 or D2)= 10% + 15% - 3%

P(D1 or D2)= 22%

P(D1 or D2)= 0.22

b)

Conditional probability that randomly selected person will get get diseases given she has contracted at least one disease is gven as

Probability= P(D1 and D2) / P(D1 or D2)

Probability=
`(0.03)/(0.22)`

Probability= 13.63%

Probability= 0.1363