Jennifer Said:

What is a good lesson plan for teaching Probability of Compound Events for 8th grade?

We Answered:

You have 2 boxes, a coin, 4 white marbles and 4 black marbles. Your life depends on arranging the marbles in the boxes. One box is marked heads and the other is tails. You put the marbles in the boxes anyway you want.
You flip the coin, then pick a marble from that box. If it's white you go free else you die. How would you arrange the marbles?

Students usually split them equally in the 2 boxes and the probability of freedom is .5

Head box - 2W , 2B P(Free) = 1/2*2/4 =1/4
Tail box - 2W, 2B P(Free) = 1/2*2/4 =1/4
and 1/4 + 1/4 = 1/2


A better solution (Hopefully A student will suggedt this) is:
Head box - 1W , 0B P(Free) = 1/2*1 =1/2
Tail box - 3W, 4B P(Free) = 1/2*3/7 =3/14
and 1/2 + 3/14 = 10/14 Much better
During the lesson there are lots of opportunities to talk about compound events whether they are dependent or independent.
Hope this helps...

Julia Said:

Financial Mini Case...........?

We Answered:

I think you should do your own homework. Any answers you get here are likely to be bogus.

Ron Said:

I need help with a probability question?

We Answered:

I believe john overcounted because he correctly assumes the first card can be any of the 52. but there are only three ways from that point.

for example if the 1st card is R7 then the ways to have the first three cards be 7's are if the next two are blue and green, blue and black or black and green (order doesn;t matter)

Another way
number of ways event can occur/total number of possible outcomes.

the total number of permutations of the 52 cards is 52! (52 ways for the first, 51 ways for the second...)

the number of ways for the first three to match are
52 ways for the first card, 3 ways for the next two card, and 49! ways for the remaining 49 card

that is 52*3*49!/52!

reduce factorial to
52*3/52*51*50 (49, 48, 47 .... all cancel)

or
156/132600 about .00117


also used Monte Carlo simulation to verify-

Edward Said:

Skittles lesson plan?

We Answered:

Dear Sky,
You have seven Skittles,
I ate one times seven,
how many do you have left?
Have a Dandy Day! [^_^]

Agnes Said:

probability help again.?

We Answered:

Probability = 47% x 78% = 36.66%