Answer:
0.699
Step-by-step explanation:
P(D \geq 2)P(D≥2)P, left parenthesis, D, is greater than or equal to, 2, right parenthesis is the probability that the first digit is 222, 333, 444, and so on, all the way up to 999.
Hint #22 / 3
Let's see how likely it is for the first digit to be 222 or higher:
DDD P(D)P(D)P, left parenthesis, D, right parenthesis DDD P(D)P(D)P, left parenthesis, D, right parenthesis
111 {0.301}0.3010, point, 301 666 \blueD{0.067}0.067start color #11accd, 0, point, 067, end color #11accd
222 \blueD{0.176}0.176start color #11accd, 0, point, 176, end color #11accd 777 \blueD{0.058}0.058start color #11accd, 0, point, 058, end color #11accd
333 \blueD{0.125}0.125start color #11accd, 0, point, 125, end color #11accd 888 \blueD{0.051}0.051start color #11accd, 0, point, 051, end color #11accd
444 \blueD{0.097}0.097start color #11accd, 0, point, 097, end color #11accd 999 \blueD{0.046}0.046start color #11accd, 0, point, 046, end color #11accd
555 \blueD{0.079}0.079start color #11accd, 0, point, 079, end color #11accd
We could add those probabilities to find our answer, but it's probably easier to use the fact that all of the probabilities add to 111, then subtract the probabilities we don't want:
P(D \geq 2)=1-0.301=0.699P(D≥2)=1−0.301=0.699P, left parenthesis, D, is greater than or equal to, 2, right parenthesis, equals, 1, minus, 0, point, 301, equals, 0, point, 699
Hint #33 / 3
The answer:
P(D \geq 2)=0.699P(D≥2)=0.699
