A bag contains 7 red chips and 10 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that both chips are red?
Once the first red chip has been picked, there are only 16 total chips and 6 red chips remaining.
To find the probability that both (all) events occur, you need to multiply the probabilities of the individual events.
7/17 * 6/16 = ?
A box contains 25 yellow, 28 green and 38 red jelly beans.
If 13 jelly beans are selected at random, what is the probability that:
a) 5 are yellow?
b) 5 are yellow and 7 are green?
c) At least one is yellow?
the anwser is 4
To find the probability that both chips are red, we need to first calculate the total number of possible outcomes, and then determine the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes
When selecting two chips from a bag without replacement, the total number of possible outcomes is given by the combination formula:
nCk = n! / (k!(n-k)!)
where n is the total number of chips in the bag (7 red + 10 blue = 17 chips) and k is the number of chips to be selected (2 chips). Let's calculate the total number of possible outcomes:
17C2 = 17! / (2!(17-2)!) = 17! / (2! * 15!) = (17 * 16) / (2 * 1) = 136.
So, there are 136 possible outcomes when selecting two chips from the bag.
Step 2: Determine the number of favorable outcomes
To have both chips be red, we need to select 2 red chips from the 7 available. The number of favorable outcomes can be calculated by:
7C2 = 7! / (2!(7-2)!) = 7! / (2! * 5!) = (7*6) / (2*1) = 21.
So, there are 21 favorable outcomes when selecting two red chips from the bag.
Step 3: Calculate the probability
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 21 / 136 ≈ 0.1544.
Therefore, the probability that both chips are red is approximately 0.1544 or 15.44%.