Answer:
a) P(NP/L) = 0.1
b) P(P/L) = 0.9
c) P(P) = 0.666
d) P(L/P) = 0.945
e) P(NL U NP) = 0.37
Step-by-step explanation:
given that;
P = passing the course, NP = Not passing the course, L = Using lab, NL = not using Lab
P(L) = 70% = 0.7, P(NL) = 30% = 0.3
P(P/L) = 90% = 0.9
P(P/NL) = 12% = 0.12
a)
the probability of not passing the course given that the student went to the Learning Lab
P(NP/L) = 1 - P(P/L)
P(NP/L) = 1 - 0.9
P(NP/L) = 0.1
b)
the probability of using the Learning Lab and passing the course
P(P/L) = 0.9
c)
the probability of passing the class
P(P) = P(P/L) * P(L) + P(P/NL) * P(NL)
= (0.9 * 0.7) + (0.12 * 0.3)
P(P) = 0.666
d)
the probability that a student utilized the Learning Lab given the condition that the student passed the class
P(L/P) = [P(P/L) * P(L)] / P(P)
P(L/P) = (0.9 * 0.7) / 0.666 = 0.63/0.666
P(L/P) = 0.945
e)
the probability of not using the Learning Lab or not passing the class
P(NL U NP) = P(NL) + P(NP) - P(NP n NL)
= 0.3 + 0.334 - (0.88 * 0.3 )
= 0.634 - 0.264
P(NL U NP) = 0.37
