Q.1 – Q.2 , Q.3 – Q.4 Q.5 , Q.6 , Q.7 , Q.9 , Q. 10 , Q. 11 Q.12 , Q.13 , Q. 14 , Q. 15 Q.16 to Q. 19
Answer 13
( a ).
Probability of selecting a junior = P ( M ) = 19/ 40
So, Probability of not selecting a junior = 1 – P ( M)
= 1 – 19 / 40
= 21/40
OR
There are 19 juniors that means 40 – 19 = 21 are not juniors
Probability of not selecting a junior = 21/40
( b ) .
Probability of a female or a Sophomores
There are total 22 females,
So, Probability of selecting a female = P (N)= 22/40
There are total 16 Sophomores and out of this, there are 10 females which we have already considered, hence here we consider males only
Probability of selecting a Sophomores = P ( L ) = 6/40
As both event are mutually exclusive , apply the formula
Probability of selecting a female or a Sophomores = P (N ∪ L)
P (N∪L) = P (N) + P (L)
P (N ∪ L) = 22/40 + 6/40
= 28/40
= 7/10
( c ).
Probability of selecting a male sophomores = P (M ) = 6/40
Probability of selecting a female senior = P ( N ) = 3/40
Both are mutually exclusive events
Probability of selecting a male sophomores or a female senior ;
P ( M ∪ N ) = P ( M ) + P ( N )
= 6 /40 + 3 /40
= 9/40
Answer 14
(a).
A and B are mutually exclusive events so,
P ( A∪ B ) = P ( A ) + P (B )
0.6 = 0.2 + P ( B )
P ( B ) = 0.6 -0.2
P ( B ) = 0.4
(b).
C and D are independent events
P ( C ∪ D ) = P ( C ) + P ( D ) – P ( C ) x P ( D )
0.6 = 0.5 + P (D) – 0.5 P(D)
0.1 = 0.5 P ( D )
P ( D ) = 0.2
Answer 15
Probability that Lin decode a message = P( M) = 0.8
Probability that Mark decode a message = P ( N ) = 0.7
Both are independent events
(a).
Both will decode the message = P ( M ∩ N ) = P ( M ) x P ( N )
= 0. 8 x 0. 7
P ( M ∩ N )= 0.56
( b ) .
At least one of them will decode the message
Probability of at least one of them will decode the message = P ( M ∪ N )
For independent events ;
P (M∪N) = P (M) + P (N) – P(M)P(N)
= 0.8 + 0. 7 – 0. 8 x 0. 7
= 1.5 – 0.56
= 0.94
( c ) .
Probability of neither of them decode the message = 1 – P(M ∪ N)
= 1 – 0.94
= 0.06
Q.1 – Q.2 , Q.3 – Q.4 Q.5 , Q.6 , Q.7 , Q.9 , Q. 10 , Q. 11 Q.12 , Q.13 , Q. 14 , Q. 15 Q.16 to Q. 19
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