Lucia is practicing shuffling cards. To make it more interesting, she decides to draw a card and note if it is a face card (Jack, Queen, King) or not. Then she puts the card back in the deck, shuffles, and draws a new card. She does this until she has drawn a total of 160 cards. Note that Lucia is using a standard 52-card deck, which has 12 face cards.

What is the probability that Lucia will get at least 40 face cards in 160 draws? Answer as a probability (between 0 and 1) to four decimal places.