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Combinatorics

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Winning on Scratcher Tickets

COMBIN-216IDV

You bought a scratcher ticket and are hoping to win some money. There are four spots you can scratch off and each spot reveals a number and a symbol. The symbol is either a cat, dog, monkey, parrot, or a big bag of money. The number is any number between 1 and 4. There are three ways you can win:

  1. All four spots have a big bag of money as a symbol.

  2. All four spots have the same number.

  3. A cat, dog, monkey, and parrot show up as a symbol and the numbers are all odd or all even.

What is the probability you have a winning ticket?

A

$\frac{3}{5^44^4}$

B

$\frac{693}{40000}$

C

$\frac{157}{8000}$

D

$\frac{214}{10000}$