There are 20 pink balloons in a bunch of 100. 34 people out of 100 like pink balloons( versus other colors). What is the probability that a person liking pink balloons gets 5 pink balloons when taking 7 random balloons from the bunch? (dependent events)
To find the probability that a person liking pink balloons gets 5 pink balloons when taking 7 random balloons from the bunch, we need to consider the concept of dependent events.
First, let's determine the probability of selecting a pink balloon on the first draw. We know that there are 20 pink balloons in a bunch of 100, so the probability of selecting a pink balloon on the first draw is 20/100 = 1/5.
Since this is a dependent event, the probability of selecting a pink balloon on the second draw depends on the result of the previous draw. After the first draw, there will be 6 pink balloons left in a bunch of 99. So, the probability of selecting a pink balloon on the second draw is 6/99.
Using the same logic, for the third draw, there will be 5 pink balloons left in a bunch of 98, so the probability of selecting a pink balloon on the third draw is 5/98. We can continue this process until the seventh draw.
To calculate the probability of obtaining 5 pink balloons in 7 draws, we need to multiply the probabilities of selecting a pink balloon on each of the seven draws together. In this case, it would be:
(1/5) * (6/99) * (5/98) * ... * (2/96)
After multiplying all of these probabilities together, you will have the probability of a person liking pink balloons getting 5 pink balloons when taking 7 random balloons from the bunch.
Keep in mind that this calculation assumes that the balloons are selected without replacement, meaning that once a balloon is selected, it is not put back into the bunch before the next draw.