A four-digit number starts with a number between 5-9 in the first position, with no restrictions on the remaining 3 digits. a right parenthesis Find the probability that a randomly-chosen phone number contains all different digits. b right parenthesis Find the probability that a randomly-chosen phone number contains at least one repeated digit.
Accepted Solution
A:
Answer:a. 0.504b. 0.496Step-by-step explanation:Given,There are 4 digit in a number,In which the possible number in first position = 3 (i.e. 6, 7, 8 )If the repetition of digit is not allowed, The possible number in second position = 9In third position = 8And, in fourth position = 7Thus, the possible ways of arranging a number in which each contains different digit = 3 × 9 × 8 × 7= 1512,While, the total possible ways of arranging 4 numbers = 3 × 10 × 10 × 10 = 3000a. Hence, the probability that a randomly-chosen phone number contains all different digits = [tex]\frac{1512}{3000}[/tex][tex]=0.504[/tex]b. The probability that a randomly-chosen phone number contains at least one repeated digit = 1 - the probability that a randomly-chosen phone number contains all different digits = 1 - 0.504= 0.496