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Any help on how to do the following probability problem would be appreciated.
Thanks
Quote:
I have planted new tulip bulbs in my front yard, but confused the colors of the bulbs. If I had 8 yellow, 6 red, 5 pink, and 5 purple tulips, what is the probability that 6 bulbs I planted will all be the same color?
Clearly they will need to be all yellow or all red.Quote:
Originally Posted by mathguy20
Calculate the probability of either event happening independently.
The easier one is to calculate the probability that all 6 will be red.
Can you evaluate that?
I see it like this:Quote:
Originally Posted by mathguy20
All 6 yellow: $\displaystyle \[\mathop C\nolimits_8^6 = \frac{{8!}}{{6! \cdot (8 - 6)!}} = 28\]$
All 6 red: $\displaystyle \[\mathop C\nolimits_6^6 = 1\]$
Successful combinations: $\displaystyle \[m = 28 + 1 = 29\]$
Total combinations (successful + unsuccessful): $\displaystyle \[n = \mathop C\nolimits_{24}^6 = \frac{{24!}}{{6! \cdot (24 - 6)!}} = 134596\]$
Therefore probability $\displaystyle \[P = \frac{m}{n} = \frac{{29}}{{134596}}\]$
Is it 6/24 that all are red and 8/24 that all are yellow?Quote:
Originally Posted by Archie Meade
There are 24 bulbs in total, so that's the denominator for the probabilities.Quote:
Originally Posted by mathguy20
You are correct for the red,
but you need Pranas' logic for the yellow.
If you plant 6 bulbs and they are all yellow,
it could be some set of 6 from the 8 yellow.
So you must select 6 of 8 first to calculate the probability of planting 6 yellow.
How many ways are there to choose 6 from 8 ?
