A package contains 9 candy canes, 6 of which are cracked. If 2 are selected, find the probability of getting no cracked candy canes.
3 out of 9?
so three are not cracked.
prob of getting 2 not cracked = 3/9)(2/8) = 1/12
or
choose 2 from the 3 non-cracked = C(3,2) = 3
choose any 2 of the 9 = C(9,2) = 36
so prob = 3/36 = 1/12
To find the probability of getting no cracked candy canes, we need to calculate the number of successful outcomes (no cracked candy canes) divided by the total number of possible outcomes.
The total number of possible outcomes is given by selecting 2 candy canes out of a total of 9. This can be calculated using combinations (denoted by C):
Total number of possible outcomes = C(9, 2) = 9! / (2! * (9-2)!) = 36
The number of successful outcomes (no cracked candy canes) is given by selecting 2 candy canes out of the 3 non-cracked candy canes. This can also be calculated using combinations:
Number of successful outcomes = C(3, 2) = 3! / (2! * (3-2)!) = 3
Therefore, the probability of getting no cracked candy canes is:
Probability = Number of successful outcomes / Total number of possible outcomes
= 3 / 36
= 1 / 12
So, the probability of getting no cracked candy canes when 2 are selected is 1/12.
To find the probability of getting no cracked candy canes, we need to calculate the probability of selecting two candy canes that are not cracked.
First, let's determine the total number of options or total number of ways to select 2 candy canes from the package. We can use the combination formula, which is given by:
nCr = n! / ((r!(n-r)!)
where n is the total number of items and r is the number of items we want to select.
In this case, we have 9 candy canes in total, so n = 9. We want to select 2 candy canes, so r = 2. Plugging in these values into the combination formula:
9C2 = 9! / ((2!)(9-2)!)
9C2 = (9! / (2! * 7!)
9C2 = (9 * 8 * 7!) / (2! * 7!)
After simplifying, we get:
9C2 = (9 * 8) / (2)
9C2 = 36
So there are 36 ways to select 2 candy canes from the package.
Next, let's determine the number of ways to select 2 candy canes that are not cracked. Since there are 6 cracked candy canes, we have 3 candy canes that are not cracked.
To calculate this, we can again use the combination formula:
3C2 = 3! / ((2!)(3-2)!)
3C2 = (3! / (2! * 1!)
3C2 = (3 * 2) / (2 * 1)
3C2 = 3
So there are 3 ways to select 2 candy canes that are not cracked.
Now, we can calculate the probability of getting no cracked candy canes by dividing the number of ways to select 2 candy canes that are not cracked by the total number of options:
Probability = Number of ways to select 2 candy canes that are not cracked / Total number of options
Probability = 3 / 36
Simplifying, we get:
Probability = 1 / 12
Therefore, the probability of getting no cracked candy canes is 1/12.