1. Consider an experiment with events [latex]A, B[latex], and [latex]C[latex] for which [latex]P(A)=0.23,P (B)=0.40, P(C)=0.85[latex], and Suppose that events [latex]A[latex] and [latex]B[latex] are mutually exclusive and events [latex]B[latex] and [latex]C[latex] are independent. What are the probabilities [latex]P(AorB)[latex] and [latex]P(BorC)[latex]?
2. In a box of [latex]10[latex] electrical parts, [latex]2[latex] are defective.
(a) If you choose one part at random from the box, what is the probability that it is not defective?
(b) If you choose two parts at random from the box, without replacement, what is the probability that both are defective?
3. A coin with heads on one side and tails on the other has a [latex]1/2[latex] probability of landing on heads. If the coin is flipped [latex]5[latex] times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order
4. The table below shows the distribution of a group of [latex]40[latex] college students by gender and class.
If one student is randomly selected from this group, find the probability that the student chosen is
(a) not a junior
(b) a female or a sophomore
(c) a male sophomore or a female senior
5. Let [latex]A, B, C[latex], and [latex]D[latex] be events for which [latex]P(AorB)=0.6, P(A)=0.2,P (CorD)=0.6, P(C)=0.5[latex], and The events [latex]A[latex] and [latex]B[latex] are mutually exclusive,. and the events [latex]C[latex] and [latex]D[latex] are independent.
(a) Find [latex]P(B)[latex]
(b) Find [latex]P(D)[latex]
6. Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is [latex]0.80[latex] and the probability that Mark will decode the message is [latex]0.70[latex], find the probability that
(a) both will decode the message
(b) at least one of them will decode the message
(c) neither of them will decode the message
7. A prize of $[latex]200[latex] is given to anyone who solves a hacker puzzle independently. The probability that Tom will win the prize is [latex]0.6[latex], and the probability that John will win the prize is [latex]0.7[latex]. What is the probability that both will win the prize?
(A) [latex]0.35[latex]
(B) [latex]0.36 [latex]
(C) [latex]0.42[latex]
(D) [latex]0.58[latex]
(E) [latex]0.88[latex]
8. If the probability that Mike will miss at least one of the ten jobs assigned to him is [latex]0.55[latex], then what is the probability that he will do all ten jobs?
(A) [latex]0.1[latex]
(B) [latex]0.45[latex]
(C) [latex]0.55[latex]
(D) [latex]0.85[latex]
(E) [latex]1[latex]
9. In a box of [latex]5[latex] eggs, [latex]2[latex] are rotten
| Quantity A | Quantity B |
| The probability that one egg chosen at random from the box is rotten | The probability that two eggs chosen at random from the box are rotten |
10. A meeting is attended by [latex]750[latex] professionals. [latex]450[latex] of the attendees are females. Half the female attendees are less than thirty years old, and one-fourth of the male attendees are less than thirty years old. If one of the attendees of the meeting is selected at random to receive a prize, what is the probability that the person selected is less than thirty years old?
(A) [latex]1/8[latex]
(B) [latex]1/2[latex]
(C) [latex]3/8[latex]
(D) [latex]2/5[latex]
(E) [latex]3/4[latex]
11. Every one who passes the test will be awarded a degree. The probability that Tom passes the test is [latex]0.3[latex], and the probability that John passes the test is [latex]0.4[latex]. The two events are independent of each other. What is the probability that at least one of them gets the degree?
(A) [latex]0.28[latex]
(B) [latex]0.32[latex]
(C) [latex]0.5[latex]
(D) [latex]0.58[latex]
(E) [latex]0.82[latex]
12. A bag contains [latex]6[latex] black chips numbered [latex]1-6[latex] respectively and [latex]6[latex] white chips numbered [latex]1-6[latex] respectively. If Pavel reaches into the bag of [latex]12[latex] chips and removes [latex]2[latex] chips, one after the other, without replacing them, what is the probability that he will pick black chip #[latex]3[latex] and then white chip #[latex]3[latex]?
13. Tarik has a pile of [latex]6[latex] green chips numbered [latex]1-6[latex] respectively and another pile of [latex]6[latex] blue chips numbered [latex]1-6[latex] respectively. Tarik will randomly pick [latex]1[latex] chip from the green pile and [latex]1[latex] chip from the blue pile.
| Quantity A | Quantity B |
| The probability that both chips selected by Tarik will display a number less than [latex]4[latex] | [latex]1/2[latex] |
14. A bag contains [latex]6[latex] red chips numbered [latex]1-6[latex] respectively and [latex]6[latex] blue chips numbered [latex]1-6[latex] respectively. If [latex]2[latex] chips are to be picked sequentially from the bag of [latex]12[latex] chips, without replacement, what is the probability of picking a red chip and then a blue chip with the same number?
Answer:
1 0.91
2 (a) 4/5 (b) 1/45
3 16
4
(a) 21/40
(b) 7/10
(c) 9/40
5 (a) 0.4 (b) 0.2
6 (a) 0.56 (b) 0.94 (c) 0.06
7 C
8 B
9 A
10 D
11 D
12 1/212
13 B
14 1/22
