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Q20
Probability,Conditional Probability
and Independence
Q1: Consider the experiment of flipping a balanced coin three times independently.
1. The number of points in the sample space is..
(A) 2 (B) 6 (C) 8 (D) 3 (E) 9
2. The probability of getting exactly two heads is…
(A) 0.125 (B) 0.375 (C) 0.667 (D) 0.333 (E) 0.451
3. The events ‘exactly two heads’ and ‘exactly three heads’ are…
(A) Independent (B) disjoint (C) equally likely (D) identical (E) None
4. The events ‘the first coin is head’ and ‘the second and the third coins are tails’ are…
(A) Independent (B) disjoint (C) equally likely (D) identical (E) None
Solution of Q1:
1)
2)
A:exactly two heads
3)
B: exactly three heads ,
4)
C: the first coin is head ,
D: the second and the third coins are tails,
.
Q2. Suppose that a fair die is thrown twice independently, then
1. the probability that the sum of numbers of the two dice is less than or equal to 4 is;
(A) 0.1667 (B) 0.6667 (C) 0.8333 (D) 0.1389
2. the probability that at least one of the die shows 4 is;
(A) 0.6667 (B) 0.3056 (C) 0.8333 (D) 0.1389
3.
the probability that one die shows one and the sum of the two dice is four is;
(A) 0.0556 (B) 0.6667 (C) 0.3056 (D) 0.1389
4. the event A={the sum of two dice is 4} and the event B={exactly one die shows two} are,
(A) Independent (B) Dependent (C) Joint (D) None of these.
Solution of Q2:
1)
2)
3)
4)
.
Q3. Assume that , then
1. the events A and B are,
(A) Independent (B) Dependent (C) Disjoint (D) None of these.
2. is equal to,
(A) 0.65 (B) 0.25 (C) 0. 35 (D) 0.14
NOTE:
Solution of Q3:
1)
2)
Q4. If the probability that it will rain tomorrow is 0.23, then the probability that it will not rain tomorrow is:
(A) 0.23 (B) 0.77 (C) 0.77 (D) 0.23
Solution of Q4:
A: it will rain tomorrow ,
Q5. The probability that a factory will open a branch in Riyadh is 0.7, the probability that it will open a branch in Jeddah is 0.4, and the probability that it will open a branch in either Riyadh or Jeddah or both is 0.8. Then, the probability that it will open a branch:
1. in both cities is:
(A) 0.1 (B) 0.9 (C) 0.3 (D) 0.8
2. in neither city is:
(A) 0.4 (B) 0.7 (C) 0.3 (D) 0.2
Solution of Q5:
A: factory open a branch in Riyadh
B: factory open a branch in Jeddah
1)
Since
2)
Or by table
A
SUM
B
SUM
1
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