Question

Actuary Tong has to study for two actuarial exams: Exam P and Exam FM. The amount of study time that Actuary Tong will spend on each exam in a day follows a continuous random variable that ranges from 0 to 1 hour. The amount of study time that Actuary Tong spends on both exams in a day has a joint density function that is equal to the sum of the study times that Actuary Tong spends on each exam in a day. Calculate the probability Actuary Tong spends at least half an hour in a day studying for exactly one of the exams

Answer 1

The Probability of spending at least half an hour on exactly one subject is mathematically given as

P(1)= 0.50

What is the Probability of spending at least half an hour on exactly one  subject

Question Parameters:

The amount of study time that Actuary Tong will spend on each exam in a day follows a continuous random variable that ranges from 0 to 1 hour.

Generally, the equation for the Probability of spending at least half an hour on a subject is mathematically given as

P(A)= (1 – 0.5)/(1 – 0)

P(A)= 0.5

Hence, the Probability of spending at least half an hour on exactly one subject is mathematically given as

P(1)=2​​​​​​C1 * 0.5 * 0.5

P(1)= 0.50

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