The credit department of Lion$$s Department Store in Anaheim,

California, reported that $24\%$ of their sales are cash, $30\%$ are paid

with a credit card, and $46\%$ with a debit card. Twenty percent of

the cash purchases, $90\%$ of the credit card purchases, and $50\%$ of

the debit card purchases are for more than $$50.$Ms$.$ Tina Stevens just purchased a new dress that cost $$120.$ What

is the probability that she paid cash?$($Round your answer to

$3$ decimal places.$)$