Answer:
(a) 0.00833
(b) 0.04167
Step-by-step explanation:
There are 5 pieces to form a car.
Total number of arrangement of these 5 pieces is, [tex]5!=5\times4\times3\times2\times1 = 120[/tex]
Of these 120 arrangements only 1 arrangement will form a proper car.
(a)
Probability that each position's guess is correct is,
[tex]P(Winning)=\frac{Favorable\ arrangements}{Total\ number\ of\ arrangements} \\=\frac{1}{120}\\ =0.00833\\\approx0.833\%[/tex]
Thus, the probability of getting all the guesses correct is 0.00833 or 0.833%.
(b)
It is given that we know the first correct piece.
That is we need to guess the other 4 from the 4 remaining pieces.
Total number of arrangement of these 5 pieces is,
[tex]4!=4\times3\times2\times1 = 24[/tex]
Of these 24 arrangements only 1 arrangement will form a correct arrangement with the known first piece.
Probability that each position's guess is correct is,
[tex]P(Winning)=\frac{Favorable\ arrangements}{Total\ number\ of\ arrangements} \\=\frac{1}{24}\\ =0.04167\\\approx4.17\%[/tex]
Thus, the probability of getting all the guesses correct when we know the first correct piece is 0.04167 or 4.17%.
The probability of winning when
The number of digits is given as:
n = 5
When you guess the position of each digit, the number of combination is:
n! = 5!
Expand
n! = 5 * 4 * 3 * 2 * 1
n! = 120
Only one of the 120 combinations is right.
So, the probability of winning is 1/120
When you guess the position of other four digits, the number of combination is:
n! = 1 * 4!
Expand
n! = 1 * 4 * 3 * 2 * 1
n! = 24
Only one of the 24 combinations is right.
So, the probability of winning is 1/24
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