Respuesta :
Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
= [tex]^nP_r[/tex]
n = 9
r = 3
= ⁹P₃
= [tex]\frac{9!}{9!-3!}[/tex]
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 × [tex]\frac{8!}{8!-2!}[/tex]
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
We will see that 504 different numbers can be formed, 56 of these start with the number 1.
And the probability of getting a number smaller than 200 is P = 0.104.
How to get the numbers of combinations?
a) 3 numbers from 1 to 9 will be selected.
- The first number can be any of the 9 options.
- The second number has 8 options (because one ball was already taken).
- The third number has 7 options (because two balls were already taken).
The number of combinations is given by the product between the numbers of options, we will get:
C = 9*8*7 = 504.
b) If the first digit is 1, then we only have options for the second and third ball. The second has 8 options and the third 7 options, then there are:
C = 8*7 = 56 combinations.
C) There are 56 combinations that are smaller than 200 (the ones that start with the digit 1). And there are 504 numbers that can be formed in total with the balls.
The probability of getting a 3-digit number smaller than 200 is given by the quotient between the number of possible numbers thar are smaller than 200, and the total number of numbers that can be formed, this is:
P = 56/504 = 0.111
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
