Suppose that you purchase a lottery ticket that contains two numbers and a lette

Question

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 if a perfect match (both digits and letter)?

I need a step by step way to figure these out.....

Explanation / Answer

Assume 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. 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.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.