SOLUTION: Suppose that you purchase a lottery ticket that contains two numbers and a letter such as 3 7 P A. What is the probability that you match the first digit? B. What is the p

Question 84798This question is from textbook Elementary Statistics in Social Research
: Suppose that you purchase a lottery ticket that contains two numbers and a letter such as
3 7 P
A. What is the probability that you match the first digit?
B. What is the probability that you match the second digit?
C. What is the probability that you do not match the first digit?
D. What is the probability that you match both the first and second digits?
E. What is the probability that you match the letter?
F. what is the probability of a perfect match (both digits and the letter)? This question is from textbook Elementary Statistics in Social Research

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Presuming that the numbers can be zero through 9 (a total of 10 numbers):
.
A. The probability of matching the first digit is 1 in 10 or 10% or 0.1
B. Similarly, the probability of matching the second digit is also 1 in 10 or 10% or 0.1
C. The probability that you do not match the first digit is 9 in 10 or 90% or 0.9
D. The probability that you do match both the first and second digits is equal to the product
of the probability of matching the first digit times the probability of matching the second
digit. This product is 0.1 times 0.1 and it equals 0.01 or 1 in 100 or 1%. You can look
at it another way. The first two digits combined could be any number from 00 to 99. This
is a total of 100 numbers and you therefore have 1 chance in 100 of getting the correct number.
E. Since there are 26 letters in the alphabet, you have 1 chance in 26 of getting the
right letter. Dividing 26 into 1 tells you that in decimal form this probability is
0.038461538 or 3.8461538%
F. The probability of getting a perfect match is the product of the three probabilities
for getting each of the numbers and the letter correct. This product is:
.
0.1 * 0.1 * 0.038461538 = 0.0003846153846 or its equivalent percent of 0.03846153846%.
.
You could also get the equivalent by multiplying:
.
(1/10)*(1/10)*(1/26) = 1/2600
.
which means you have a 1 in 2600 chance of getting all three correct. This also means that
on average you should get it correct once in every 2600 times you try drawing the numbers
and the letter.
.
Hope this helps you to understand probability a little better.
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