Hi Electric Pavlov,
I'm going to have a go too :)
1) 2 standard 6-sided dice are rolled. What is the probability that the sum rolled is a perfect square?
ElectricPavlov has nailed it!
2) A card is drawn at random from a standard 52-card deck. What is the probability it is an odd number or a spade?
This one can be interpreted differently so it is a bad question....
I am going to consider odd numbers to be 3,5,7,9 there are 4*4=16 of these
There are 13 spaces and there are 4 odd spades so
P=(16+13-4)/52 = 25/52
3) A penny=1, nickel=5, and dime=10 are simultaneously flipped. What is the probability that heads are showing on at least 6 cents worth of coins?
dime and any other=0.5 nickel and penny but not dime= 0.5*0.5*0.5 = 0.125
So the prob will be 0.625 or 5/8
AGAIN ElectricPavlov nailed it! :)
4) 8 coins are simultaneously flipped. What is the probability that heads are showing on at most 2 of them?
P(none)+P(1head)+P(2heads)
\(= 8C0 * 0.5^8 + 8C1 * 0.5^8 + 8C2 * 0.5^8\\ = 1 * 0.5^8 + 8 * 0.5^8 + 28 * 0.5^8\\ = (1+8+28) * 0.5^8 \\ = 37* 0.5^8 \\\)
37*0.5^8 = 0.14453125
5) 5 white b***s and k black b***s are placed into a bin. Two of the black b***s are drawn at random. The probability that one of the drawn b***s is white and the other is black is .
\(\mbox{P(one white and one black)=}2(\frac{5}{5+k}*\frac{k}{5+k})=\frac{10k}{(5+k)^2}\)
Please ask if you would like more explanationg :)