A standard deck of playing cards is made up of $26$ red cards and $26$ black cards. Robbie shuffles and deals a card and records its color. She replaces the card in the deck and repeats this process $25$ times, obtaining $10$ red cards and $15$ black cards - only $40\%$ red!
Does Robbie have reason to believe the deck of cards has an unusually small proportion of red cards?
Calculate the probability of obtaining a sample proportion less than or equal to $0.4$.