Answer:
(a) 0.93
(b) 0.38
Step-by-step explanation:
A attends class 30% of the time, so DO NOT attend 70%
B attends class 50% of the time, so DO NOT attend 50%
C attends class 80% of the time, so DO NOT attend 20%
Writing as probabilities:
P(A) = 0.30 and P(A') = 0.70
P(B) = 0.50 and P(B') = 0.50
P(C) = 0.80 and P(C') = 0.20
(a) the probability that at least one of them will be in class on a particular day
Let's call Q the event of none of them be in class on a particular day
Probability of at least one be in class is the complement of none of them be there, so: 1 - P(Q)
P(Q) = 0.7*0.5*0.2 = 0.07
1 - P(Q) = 1 - 0.07 = 0.93
(b) the probability that exactly one of them will be in class on a particular day?
One of them exactly be in class is
A is B not C not or A not B is C not or A not B not and C is, so
P(A).P(B').P(C') + P(A').P(B).P(C') + P(A').P(B').P(C)
0.3*0.5*0.2 + 0.7*0.5*0.2 + 0.7*0.5*0.8 =
0.03 + 0.07 + 0.28 = 0.38
