The number 1-50 are placed in a bag. What is the probability of selecting: A) a number greater than 50
B) multiple of 5
C) a prime number
D) a composite number

Answers:

Nearly all of those answers involve a fraction form and an equivalent decimal form.

Work Shown:

Part A

The largest number in the bag is 50, so we cannot select anything larger than that. The probability of getting something larger than 50 is 0% which converts to the decimal form 0

Part B

List out the multiples of 5 to get {5,10,15,20,25,30,35,40,45,50}

Note how 50/5 = 10, which shows there are 10 multiples listed above.

We have 10 items in that set out of 50 items in the set {1,2,3,...,49,50}. The probability of getting a multiple of 5 is 10/50 = 1/5. This converts to the decimal form 0.2

Part C

The prime numbers between 1 and 50 are:

{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}

There are 15 items in that list out of 50 items in the bag, so 15/50 = (5*3)/(5*10) = 3/10 is the answer. Converting to decimal form gets us 3/10 = 0.3

Part D

There are 50 items in the bag and 15 primes. This means there are 50-15 = 35 composite items. Well this is close to the actual count. It turns out that the number "1" is not composite, and it's not prime either. So we really have 35-1 = 34 composite values.

We get 34/50 = (17*2)/(25*2) = 17/25 as the answer. That converts to 17/25 = 0.68

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