Tuesday, March 3, 2015
Unizor - Probability - Easy Problems 4
Three students were preparing for an exam that contained 100 questions.
The first student was lazy and prepared for only 50 questions out of 100.
The second student was reading an interesting novel he had to finish before preparing for an exam, he managed to prepare for 75 questions.
The third student tried hard, was about to finish all the questions, but at the last day preceding an exam he met a girl and could not finish his preparations, so he was ready for 90 questions.
At exam each student has randomly chosen one question.
Calculate the probabilities of the following events:
(a) all students got questions they have prepared for;
(b) all students got questions they have not prepared for;
(c) exactly one student got a question he was not prepared for;
(d) at least one student got a question he was not prepared for.
Consider a standard deck of card. It contains cards of four suits (Spades, Hearts, Diamonds and Clubs), each suit has cards with numbers from 2 to 10 (let's call this group of cards Numerics) and cards with pictures - Jack, Queen, King and Ace - that we will call Pictures.
So, we have 36 Numerics and 16 Pictures in the deck.
(a) We randomly pulled one card from the standard deck and it happened to be Numeric.
What is the probability that the second card randomly pulled after that is Numeric?
(b) We randomly pulled one card from the standard deck and put it aside without looking.
Then we randomly pulled the second card and it happened to be Numeric.
What is the probability of the first card to be Numeric?
(c) We randomly pulled all cards except one without looking.
What is the probability of the last one to be Numeric?
Using the same standard deck of cards determine the probability of randomly picking 13 cards out of 52 such that among them are all four Aces, all four Kings, all four Queens and any one Jack (the strongest possible hand in the game of bridge if contract specifies no trump suit).