Question

Homework in probability theory Variant 2 A box contains 10 resistors, 6 diodes and 4 capacitors. 1. 2 parts are taken from the box. Consider the following events: A) the first part is resistor B) the first part is diode C) the first part is capacitor Find the following probabilities a) p(A)-? D) the second part is resistor E) the second part is diode F) the second part is capacitor 2. Find probabilities to take a) 2 resistors We have taken 2 parts form the box. What are probabilities that we have taken a) at least one resistor b) 2 diodes c) one diode and one capacitor 3. b) at least one diode c) at least one capacitor 4· There are 20 students in the group, 8 students have excellent preparation for the exam, 6 have good level of knowledge, 4 have average level of knowledge, and 2 are bad prepared. Probability that student pass the exam for excellently prepared student is 100%, if student have good level of knowledge-90%, for average level of knowledge it is 60%, and for bad prepared student it is 20%. a) Find probability that student from this group pass the exam. Student has passed the exam. Find probabilities that this student has b) excellent preparation d) average level of knowledge c) good level of knowledge e) bad preparation

Answer 1

Resistors, R = 10

Diodes, D = 6

Capacitors, C = 4

1.

a. P(A) = Resistors in the box/Total parts = 10/20 = 1/2

b. P(B) = Diodes in the box/Total parts = 6/20 = 3/10

c. P(C) = 4/20 = 1/5

d. P(D/A) = 9/19

e. P(D/B) = 10/19

f. P(D/C) = 10/19

g. P(E/A) = 6/19

h. P(E/B) = 5/19

i. P(E/C) = 6/19

j. P(F/A) = 4/19

k. P(F/B) = 4/19

l. P(F/C) = 3/19

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