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### Probability Exercise with Answer | Example 3

Probability Exercise A bowl contains n black balls (n ∈   N *)  and two oval balls. We draw two balls in a row from this bowl without repeating before the next drawing. 1. What is the probability of drawing two white balls? 2. We denote by U n the probability of drawing two balls of the same color. a) Express U n in terms of n. b)  Calculate:                           * Interpret the result. The solution 1. Calculate the probability of drawing two white balls. We call event A: “drawing two white balls . ” and from it: P(A) is the number of appropriate cases for the event A division The number of possible cases for this experiment. 2. Calculate the probability of drawing two balls of the same color. We call event B: “Two balls of the same color are drawn.” We call the event N: “drawing two black balls.” We have:  P(B)= P(A)+P(N) So: So:                                    b) Calculate:                           * Interpretation of the result. This result is interpreted as when the n

### Probability Exercise with Answer | Example 2

Probability Exercise  A bowl contains 8 white balls, 4 black balls and 3 red balls. We randomly draw 3 balls from this bowl. What is the probability of getting: 1. A white ball and two red balls. 2. Two black balls. 3. At least a white ball. 4. Three balls of the same color. The solution 1.   The number of possible cases for this experiment is:   The number of appropriate cases is:  And from it  P 1 = 24/455 2. The number of suitable cases is:                   And from it   P 2 = 66/455 3. The mutually exclusive event of event A: ''Three balls of the same color'' is the event Ā : " : ''We don't get any white ball" We have:         And from it: 4. Number of suitable cases:                    And from it    P 4 = 61/455

### Probability Exercise with Answer | Example 1

Probability Exercise Note : parts 1 and 2 of the exercise can be done separately. The results are given in the form of fractions. 16 passengers booked tickets in Terminal A so that: 7 of them go to station B (50 dollars per ticket). 5 of them go to station C (60 dollars per ticket). 4 of them go to Terminal D (75 dollars per ticket). 1. We randomly choose one of these travelers.  Let X be the random variable that attaches to each passenger the price of his ticket in dollars. a) Determine the probability law for the random variable X b) Calculate the expected value of the random variable X. 2 . We randomly choose three of these travelers. a) Calculate the probability that these travelers will have different directions. b) Calculate the probability that at least one passenger will be heading towards station B. c) What is the probability that the direction of the three passengers will be station B, given that they are traveling in the same direction. The solution 1. We have X is the rand

### The Puzzle of Separating X from O

The puzzle of separating X from O We have the next square with four columns and four lines drawn on a square of paper that includes all of the paper. Each square contains a X sign or O sign as shown in the figure. What is required is to do one straight line cut in order to separate the X and O signs from each other as they will become separate as shown in the figure below. (The secret lies in the way the paper is folded before cutting).