A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

1 in 16,807 chance or a 0.00595% chance

Step-by-step explanation:

There is only one correct 5-digit pin that the thief must guess. If there are 7 possible values for each of the five digits, the total number of combinations is:

Therefore, there is a 1 in 16,807 chance or a 0.00595% chance that the thief will guess on the first try.

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step-by-step explanation:

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft