
Concept explainers
a.
To obtain: The
a.

Answer to Problem 14.26E
The probability of winning a bet on red colored is 0.47.
Explanation of Solution
Given info:
The roulette wheel consists of 38 slots numbered as 0, 00 and 1 to 36 in which 0,00 are green colored, 18 are red colored and 18 are black.
Calculation:
Here, the
The probability of winning a bet on red in a single play of roulette is,
Thus, the probability of winning a bet on red colored is 0.47.
b.
To obtain: The distribution of random variable X.
b.

Answer to Problem 14.26E
The distribution of X is binomial.
X | 0 | 1 | 2 | 3 | 4 |
0.0789 | 0.2799 | 0.3723 | 0.2201 | 0.0488 |
Explanation of Solution
Given info:
A bet is placed on red, every time when the roulette is played for four times.
Calculation:
Define the random variable X as the number of win, when bet is placed on red every time.
Also, there are two possible outcomes (winning the bet on red or losing the bet on red) and the probability of success is the probability that winning when placing bet on red each time (p) is 0.47 and not winning, when placing bet on red each time is 0.53
Therefore, winning when placing bet on red every time follows the binomial distribution with sample size
Thus, the value of n and p, if X has a binomial distribution is 4 and 0.47 respectively.
The probability value when
The binomial distribution formula is,
Substitute
Thus, the probability value with
The probability value when
Substitute
Thus, the probability value with
The probability value when
Substitute
Thus, the probability value with
The probability value with
Substitute
Thus, the probability value with
The probability value with
Substitute
Thus, the probability value with
Thus, the probability distribution of X is given below:
X | 0 | 1 | 2 | 3 | 4 |
0.0789 | 0.2799 | 0.3723 | 0.2201 | 0.0488 |
c.
To find: The probability of break even.
c.

Answer to Problem 14.26E
The probability of break even is 0.5.
Explanation of Solution
Given info:
Break even means when same amount of bet is placed on every play and win exactly two plays out of four plays.
Calculation:
Thus, the probability of break even is 0.5.
d.
To find: The probability of losing money.
d.

Answer to Problem 14.26E
The probability of losing money is 0.3125.
Explanation of Solution
Given info:
In four plays, fewer than two are won then money will be lost.
Calculation:
Define the random variable Y “number of times the game is lost”
From part (c) the probability of losing, p is 0.5 thus, q is
The probability value for
The binomial distribution formula is,
Substitute
Thus, the probability of losing money is 0.3125.
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Chapter 14 Solutions
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