Page 186 - Engineering Mathematics Workbook_Final

Probability & Statistics

136. If the probability that a 0.95 and the probability that a
communication system has a high transmitted ‘1’ is received as a ‘1’ is
fidelity is 0.81 and the probability 0.90. If the probability that a ‘0’ is
that it will have high fidelity and high transmitted is 0.4, find the probability
selectivity is 0.18. What is the that

probability that a system with high
fidelity will also have high (i) a ‘0’ is received
selectivity? (ii) a ‘1’ is received

2 3 (iii) a ‘1’ was transmitted given that a
(a) (b)
9 9 ‘1’ was received.

4 5 (iv) a ‘0’ was transmitted given that a
(c) (d)
9 9 ‘0’ was received.

137. An unbalanced die (with six faces, 140. The probability that a student knows

numbered from 1 to 6) is thrown. The the correct answer to a multiple
probability that the face value is odd choice question is 2 . If the student
is 90% of the probability that the face 3
value is even. The probability of does not know the answer, then the
getting an even numbered face is student guesses the answer. The
same. If the probability of face is probability of guessed answer being
even, given that it is greater than 3, is 1
0.75. What is the probability that the correct is 4 . Given that the student

face value exceeds 3? has answered the question correctly,
the conditional probability that the
Baye’s Theorem
student knows the correct answer is

138. The chances that doctor A diagnoses
a disease X correctly is 60%. The (a) 2 (b) 3
chances that a patient will die by his 3 4
treatment after correct diagnosis is 5 8
40% and the chances of death by (c) 6 (d)
9
wrong diagnosis is 70%. A patient of
doctor A who had disease X died. Random Variables
What is the probability that his

disease was diagnosed correctly? 141. A fair coin is tossed until a head or
four tails occur. The expected number
139. For a certain binary communication of tosses required is _______.
channel, the probability that a
transmitted ‘0’ is received as a ‘0’ is

184