A student has a somewhat unreliable alarm clock The alarm cl

A student has a somewhat unreliable alarm clock. The alarm clock will ring at the

pre-set time with probability 0.7. If it rings, the student wakes with probability 0.8. If it does not

ring, the probability that the student wakes at that time anyway is 0.3.

(a)Define appropriate events.

(b)What is the exact probability that the student wakes at the pre-set time?

(c)If the student woke at the pre-set time, what is the exact probability that the alarm rang?

Solution

A)THE PROBABILITY THAT ALARM WILL RING = 0.7

PROBABILITY ARAM WILL NOT RING=0.3

PROBABILITY THE STUDENT WILL WAKE UP BY RINGING ALARM =0.8

PROBABILITY THE STUDENT LL WAKE UP WITHOUT RINGING ALARM = 0.3

B)WHEN ALARM RINGS PROBABILITY = 0.7*0.8

THE ALARM DOES NOT RING AND STUDENT WAKES UP = 0.3*0.3

TOTAL PROBABILITY = 0.56+0.09=0.65

C)0.56/0.65