find the probability

Question

A gardener has 9 tulip, 7 daffodil and 5 crocus bulbs to plant. If he selects 3 bulbs at random to sow what is the probability he sows:
i. 2 tulips and a daffodil? 
ii. 3 of the same flower? 
iii. At least two tulips?

 

 

Answer 1

Hello Claire! The easiest way to answer this problem is by a tree diagram. Start with 3 limbs(tulip, daffodil, and crocus). The probabilies for this limb is number of flowers/n. So Tulip is 9/21, daffodil is 7/21, and crocus 5/21). Each of the initial limbs will have 3 additional limbs with the same bulbs to represent the 2nd selection, but remember to reduce the denominator to 20 because this is sampling without replacement. Also if you picked the flower the first time, the numerator would be reduced by 1. For example the limb tulip, tulip would have a probability of 8/20 on the 2nd limb. This is a lot to explain without seeing my tree, so please message me on Wyzant's message board. Have a good one now!