A jar consists of 21 sweets, 12 are green and 9 are blue. William picked 2 sweets at random. Find the probability that both sweets are blue.
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
If there is no replacement,
9/21 * 8/20 = ?
To find the probability that both sweets are blue, we need to determine the ratio of blue sweets to the total number of sweets.
Total number of sweets = 21
Number of blue sweets = 9
The probability of picking the first blue sweet is 9/21.
After picking the first blue sweet, there are now 20 sweets left in the jar, with 8 blue sweets remaining.
The probability of picking the second blue sweet is 8/20.
To find the probability that both sweets are blue, we multiply the probabilities of each event:
P(both sweets are blue) = (9/21) * (8/20)
Simplifying this expression, we have:
P(both sweets are blue) = (3/7) * (2/5)
P(both sweets are blue) = 6/35
Therefore, the probability that both sweets are blue is 6/35.
To find the probability that both sweets William picked are blue, we need to know the total number of ways he can pick 2 sweets from the jar.
The total number of ways to pick 2 sweets out of the jar can be calculated using the combination formula, which is:
C(n, r) = n! / (r! * (n-r)!),
where n is the total number of sweets in the jar and r is the number of sweets being picked.
In this case, since William is picking 2 sweets from a jar of 21, we can calculate the total number of ways as:
C(21, 2) = 21! / (2! * (21-2)!)
Simplifying this expression gives:
(21 * 20) / (2 * 1) = 210
So, there are 210 different ways that William can pick 2 sweets from the jar.
Now, to find the probability that both sweets are blue, we need to determine the number of favorable outcomes (i.e., the number of ways William can pick 2 blue sweets) and divide it by the total number of possible outcomes.
Since there are 9 blue sweets in the jar, the number of ways to pick 2 blue sweets can be calculated using the combination formula again:
C(9, 2) = 9! / (2! * (9-2)!)
Simplifying this expression gives:
(9 * 8) / (2 * 1) = 36
So, there are 36 different ways that William can pick 2 blue sweets from the jar.
Finally, we can calculate the probability:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 36 / 210
= 6 / 35
Therefore, the probability that both sweets William picked are blue is 6/35.