Question

On a game show, you are given five digits to arrange in the proper order to form the price of a car. If you are correct, then you win the car. What is the probability of winning, given the following conditions?
(a) You guess the position of each digit.
(b) You know the first digit and guess the positions of the other digits.

Answer 1

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, $5!=5\times4\times3\times2\times1 = 120$

Of these 120 arrangements only 1 arrangement will form a proper car.

(a)

Probability that each position's guess is correct is,

$P(Winning)=\frac{Favorable\ arrangements}{Total\ number\ of\ arrangements} \\=\frac{1}{120}\\ =0.00833\\\approx0.833\%$

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,

$4!=4\times3\times2\times1 = 24$

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,

$P(Winning)=\frac{Favorable\ arrangements}{Total\ number\ of\ arrangements} \\=\frac{1}{24}\\ =0.04167\\\approx4.17\%$

Thus, the probability of getting all the guesses correct when we know the first correct piece is 0.04167 or 4.17%.