Hi,
Best to separate what we have to work with: rules, principals,distributions,
definitions, rules governing combinations & permutations etc
and what decisions need to made to apply what we have to work with.
First question is handled using the definition of the mean and standard deviation
for a Bionaomial Distribution
STATISTIC QUESTION:CONSIDERED A BINOMIAL RANDOM VARIABLE WHERE THENUMBER OF
TRIALS IS 12 AND THE PROBABILITY OF SUCCESS ON EACH TRIAL IS 0.25 .
FIND THE MEAN AND STANDARD DEVIATION OF THE RANDOM VARIABLE.
P = nCx** where p and q are the probabilities of success and failure
respectively. In this case both p = .25 or 1/4
nCx =
Definition of mean = n*p = 12*(1/4) = 3
Definition of standard deviation =
Second question: How many different combinations
"IF I GO INTO AN ICREAM PARLOR ,AND I HAVE THE CHOICE OF HAVING ONE OF 10 DIFFRENT FLAVORS , WITH ONE OF 5 TOPINGS AND ONE OF 3 DIFFRENT TYPES OF CONES, HOW MANY TIMES CAN I COME BACK TO THIS PLACE AND GET A DIFFRENT ICE CREAM CONE COMBINATION?
Flavors = 10 Toppings = 5 Cone type = 3
different combinations of ice cream cones =10*5*3 = 150
Third question: Probability involving "and"
3THERE ARE 10 COLORED BALLS IN A BOX(5RED,3BLUE,2GREEN). WHAT IS THE PROBABILITY
OF PICKING OUT THE RED BALL THEN A BLUE BALL (IF I DONOT REPLACE THE RED BALL)?
P(first is a red ball)= 5/10 or 1/2
P(Blue ball with a red one on gone)= 3/9 or 1/3
P(red and then blues)= (1/2)*)1/3) =1/6
Hope this helps.