(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. Suppose we roll 10 fair 6-sided dice. What is the probability that there are exactly two 2's showing?

2. Suppose we are dealt five cards from a standard 52-card deck. What is the probability that

a) we get all 4 aces and the king of spades

b) all 5 are spades

c) we get no pairs (all are different values)

d) a full house (3 of a kind and 2 of a kind)

2. Relevant equations

This one is correct:

there are 2 pots

in pot1 there is 5 red balls and 7 blue balls

in pot2 there is 6 red balls and 12 blue balls

3 balls are chosen randomely from each pot

chances of all 6 balls to be same color = P(A)

chances of all 6 balls to be red = P(B)

chances of all 6 balls to be blue = P(C)

P(A) = P(B or C)

=P(B) + P(C) -0

P(B)=|B|/|S| = |B|/(12choose3)(18choose3) =

(5choose3)(7choose0)(6choose3)(12choose0)/(12choose3)(18choose3) = 5/4488

P(C)=|C|/|S| = |C|/(12choose3)(18choose3) =

(5choose0)(7choose3)(6choose0)(12choose3)/(12choose3)(18choose3) = 35/816

P(A) = 5/4488 + 35/816 - 0 = 395/8976

3. The attempt at a solution

1.

number of outcomes = 6^10 = 60466176

10!/2!8! = 45

so i get

45/60466176

2.

number of outcomes = 52x51x50x49x48 / 5x4x3x2x1 = 2598960

a) Here i have two different methods, i don't know if both are wrong or one is right...

method 1

(4choose1 * 4choose4 ) / 2598960 = 1/649740

method 2

( (13choose1) * (13choose1) * (13choose1) * (13choose1) ) / 2598960 = ~0.066

b)

(13choose5)/2598960 = ~4.95x10^(-4)

c)

( (4choose1)*(4choose1)*(4choose1)*(4choose1)*(4choose1) ) /2598960 = ~3.95x10^(-4)

d)

(4choose3)*(4choose2) /2598960 = 1/108290

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help with probability problems!

**Physics Forums | Science Articles, Homework Help, Discussion**