If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?
\( \dfrac{1}{72} \)
Six new employees, two of whom are married to each other, are to be assigned six desks in a row. If the assignment is made randomly, what is the probability that the married couple will have nonadjacent desks?
\( \dfrac{2}{3} \)
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
0.556
An experiment consists of rolling a die until a 2 appears.
(i) How many elements of the sample space correspond to the event that the 2 appears on the \(k^{th}\) roll of the die?
(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the \(k^{th}\) roll of the die?
(i) \(5^{k-1}\) elements
(ii) \( \dfrac{5^{k} - 1}{4} \)
A die is loaded so that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll.
\( \dfrac{4}{9} \)
In a large metropolitan area, the probabilities are .87, .36, .30 that a family owns a colour TV, a black & white TV, or both kinds of sets. What is the probability that a family owns either one or both kinds of sets?
0.93
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
(a) P(A')
(b) P(B')
(c) P(A ∪ B)
(d) P(A ∩ B)
(e) P(A ∩ B')
(f) P(A' ∩ B')
(a) 0.65
(b) 0.55
(c) 0.8
(d) 0
(e) 0.35
(f) 0.2
A team of medical students assisting surgeries rates them as very complex, complex, routine, simple and very simple with respective probabilities 0.15, 0.20, 0.31, 0.26, 0.08. Find the probabilities that a particular surgery will be rated:
(a) complex or very complex
(b) neither very complex nor very simple
(c) routine or complex
(d) routine or simple
(a) 0.35
(b) 0.77
(c) 0.51
(d) 0.57
Four candidates A, B, C, D apply for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are equally likely, while C is twice as likely to be selected as D, determine:
(a) P(C selected)
(b) P(A not selected)
(a) \( \dfrac{2}{9} \)
(b) \( \dfrac{5}{9} \)
One of four persons John, Rita, Aslam or Gurpreet will be promoted next month. You are told John and Gurpreet have equal chance, Rita’s chances are twice John’s, and Aslam’s chances are four times John’s.
(a) Determine P(John promoted)
(b) P(Rita promoted)
(c) P(Aslam promoted)
(d) P(Gurpreet promoted)
(e) If A = {John promoted or Gurpreet promoted}, find P(A).
(a) \( \dfrac{1}{8} \)
(b) \( \dfrac{1}{4} \)
(c) \( \dfrac{1}{2} \)
(d) \( \dfrac{1}{8} \)
(e) \( \dfrac{1}{4} \)
The Venn diagram shows three events A, B, C with probabilities of intersections given. Determine:
(a) P(A)
(b) P(B ∩ C')
(c) P(A ∪ B)
(d) P(A ∩ B')
(e) P(B ∩ C)
(f) Probability that exactly one of the three occurs.
(a) 0.20
(b) 0.17
(c) 0.45
(d) 0.13
(e) 0.15
(f) 0.51