Quote:
Originally Posted by sri340  A cave contains 2 brown bats and 3 gray bats. The bats fly out of the cave one at a time. What is the probability that the fourth bat to fly out of the cave is gray? Express your answer
as a common fraction. |
The easiest way to to make a probability tree.
Here is that one, listing all the possible outcomes for the first four bats. [Sorry it's so huge
]
1. You can have either brown or black (from left to right), so, probability of having brown = 2/5 and that of grey is 3/5
2. Following each kind of possibility, the probability changes accordingly. For example, if a brown bat was the first one, (going though the upper branch), you have 1 brown left and 3 greys, with total of 4. So, P(brown) = 1/4 and P(grey) = 3/4, etc.
3. When all of one colour has gone out, only one remains. This happens if the two browns go first, only grey remain.
4. The probability of an event is given by multiplying each probability assigned to each branch you followed. For example, in the event that you have b, b, g, g (b=brown, g=grey) the probability is 2/5 * 1/4 * 1 * 1 = 1/10
5. For your answer, find all the outcomes where the 4th bat is grey, and add the probabilities up, because it is either one, or the other.
If you have questions, feel free to ask. I know that it's quite difficult to understand this if it is the first time.
Linear Mode
