Thread: Yucky weird probability stuff

So i am doing stuff with mutually exclusive and inclusive probabilities. For some reason, whatever i do, i seem to do it wrong. For example, this problem says "There are 5 pennies, 7 nickels, and 9 dimes in an antique coin collection. If two coins are selected at random and the coins are not replaced, find P(2 nickels or 2 silver colored coins)." So...what i thought was to find the two probablities (7 nCr 1 * 6 nCr 1/ 21 nCr 2)+ (16 nCr 1 * 15 nCr 1/ 21 nCr 2), which gets me something like 937/1470, while the answer is 4/7. What am i doing wrong? And could anyone show it in this problem possibly? "There are 5 male and 5 female students in the executive council of the Douglas High School honor society. A committee of 4 members is to be selected at random to attend a conference. Find P(at least 3 females)." Thanks a bunch!

4/7 is correct. We have 21 coins in the jar, the probability of gettin a nickle is 7/21 the probability of getting a dime is 9/21. The probability of a dime or nickle is the sum of the dime and nickel probability or 16/21.

With me so far

If you get a silver on the first draw then there are 20 coins left. 5 pennies and 15 silver coins. The odds of getting a silver coin is now 15/20.

Multiply the 2 probabilities together and you have (16/21)* (15/20) and you will get (240/420) which should simplify to 4/7.

For this problem I would draw a tree diagram to see the solution, if you think it will help you, post back and I will post a tree diagram. Problems like this are much easier to see visually

yeah, after today, i finally understood exclusive and inclusive events. Before, I tried to multiply them together i think, instead of adding the probabilities of the two events. I'm a dummy. I figured out the other problem as well.

Smarter than me. I dont even now what exclusive and inclusive mean. I just know how to handle "and" and "or"

If your ever bored please explain inclusive and exclusive to me in real words so that I might understand it.

when an event is mutually exclusive, it means that they don't affect the other event, i.e. spinning a spinner and rolling a dice. You can think of it as two circles not touching. For inclusive, it means that some of the answers fit into both categories, i.e. pick either a black card or an ace.