AMERICAN SCHOOL FOUNDATION A.C.
Probability and Statistics WORKSHEET
JAnuary 2006
1.-Box I contains 3 red and 2 blue marbles while box II contains 2 red and 8 blue marbles
A fair coin is tossed. If the coin turns up heads a marble is chosen from box I; if it turns up tails a marble is chosen from box II.
Find the probability that a red marble is chosen.
2.-In the problem above find the probability the coin turned up was heads if the marble chosen was red.
3.- How many ways can 10 people be seated on a bench if only 4 seats are available?
4.-How many four digit numbers can be formed with the ten digits( 0,1...9) if repetition are allowed?
5.-In the problem above how many numbers can be formed if repetitions are not allowed?
6.-In the problem above how many numbers can be formed if the last digit must be zero? And repetitions are not allowed?
7.-Out of 5 mathematicians anf 7 physicists a committee consistent of two mathematicians
and 3 physicists is to be formed. In how many ways can this be done?
8.- Out of 5 mathematicians and 7 physicists a committee consistent of two mathematicians and 3 physicists is to be formed.
In how many ways can this be done if one particular physicist must be on the committee?
9.- Out of 5 mathematicians and 7 physicists a committee consistent of two mathematicians and 3 physicists is to be formed.
In how many ways can this be done if two particular mathematicians can not be in the Committee?
10.- How many different salads can be made from: lettuce, escarole, endive, watercress and
Chicory? ( the salad could be with one , two....or five components)
11.- In a game of poker 5 cards are drawn from a pack of 52 cards. Find the probability that 4 kings are in a hand.
12.- In a game of poker 5 cards are drawn from a pack of 52 cards. Find the probability that 3 are tens and 2 are jacks.
13.- In a game of poker 5 cards are drawn from a pack of 52 cards. Find the probability that 4 are aces and 1 is a king.
14.- Determine the probability of obtaining three 6’s in five tosses of a fair die.
15.- The probabilities that a husband and wife will be alive in 20 years from now are
given by 0.8 and 0.9 respectively Find the probability that in 20 years for now at least one will be alive.