A vase contains purple, pink and yellow flowers.  You and a friend are both allowed to choose one flower each from the vase to take home.  You choose a flower first and then your friend chooses a flower. The probability that you choose a purple flower and then your friend chooses a yellow flower is 0.629.  The probability your friend picks a yellow flower after you choose a purple is 0.85. The probability, to the nearest hundredth, that you choose a purple flower is

You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.

you deal a hand of five cards from a regular deck of playing cards. find the probability of dealing a hand consisting of four of a kind.

Katherine works at a grocery store and is assigned their daily duty by the shift manager in charge. When Kim is the shift manager, Katherine is assigned the cash register 85% of the time. When Sophia is the shift manager, Katherine is assigned the cash register 30% of the time. The probability that Kim is the shift manager is and the probability that Sophia is 3 the shift manager is. Determine the probability, to the nearest hundredth, that Katherine works the cash register.