# Combinations in probability

• Feb 19th 2009, 03:00 PM
HFBA
Combinations in probability
1. Joseph throws two dice, one blue and the other yellow, both numbered from 1 to 6. The probability that the blue die rolls a higher number than the yellow die is?

2. 10 cards numbered 1 to 10 are placed in a box. First, Joseph picks a card randomly and then Mary picks one, also randomly. What is the probability that the sum of Joseph and Mary's cards is an even number?
• Feb 19th 2009, 04:12 PM
Plato
$\begin{gathered}
(2,1) \hfill \\
(3,2),(3,1) \hfill \\
(4,3),(4,2),(4,1) \hfill \\
(5,4),(5,3),(5,2),(5,1) \hfill \\
(6,5),(6,4),(6,3),(6,2),(6,1) \hfill \\
\end{gathered}$
• Feb 22nd 2009, 07:06 PM
matheagle
2. There are ${10\choose 2}=45$ equally likely pairs, ignoring order and who picked what.
We need to figure out which of these pairs are even and which are odd.
At first I thought the answer should be .5. But we have 45 sample points.
List them as above
(1,2).....(1,10)
(2,3).....(2,10)
.
.
(9,10)
and figure how many are even and odd.
Take the number of even ones divided by 45 should be the answer.
I counted across and think there are 20 even favorable simple events.
Look it over, if that's correct, the answer is 20/45=4/9.
• Feb 23rd 2009, 01:25 AM
An alternative to listing all the possible pairs is to say that out of the 36 possible ways in which two dice can land, 6 show equal scores. In half of the remaining 30 ways, the blue die's score will be higher than the yellow. That's 15 out of 36 altogether, giving a probability of $\frac{15}{36}= \frac{5}{12}$.