Probability

# Complements: Level 1 Challenges

A fruit basket contains only apples, oranges and mangos. All of the fruits are apples except four of them, all of the fruits are oranges except five of them, and all of the fruits are mangos except seven of them. How many fruits are there in the basket in all?

How many positive integers less than 101 contain two different digits?

Do not include leading zeros when counting the digits

4 brothers are told to stand in a row for their family portrait. Their heights are:

• Abe: 4'6''
• Ben: 4'
• Clark: 3'6''
• Dan: 3'

There's also a "Happy Birthday Dad!" poster that has to be held by 2 brothers standing next to each other, and in order to hold it straight, those two brothers have to be at most 6'' apart in height.

Mom's a bit crazy and wants to take a bunch of pictures so she has her sons stand in all 4! possible orders (ABCD, DCBA, DCAB, ... etc.) In how many of the shots can the poster be held evenly?

Alex tells the truth 70% of the time while Blake tells the truth 80% of the time, independently of each other. They are shown an apple and asked "Is it an apple or a banana?". What is the probability that they will give different answers?

Randomly pick a whole number between 10 and 99 (inclusive). Then multiply the digits together. What is the chance that the resulting number is even?

Hint: An odd number times an odd number is an odd number.

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