Seven chips labeled A B C D E F and G are placed in a jar. Five chips are drawn at random.
Find the probability thatc chips A and B are selected.
number of ways to draw 5 chips from 7 = C(7,5)
= 21
number of ways to draw the A and B and any 3 others
= 1xC(5,3) = 10
so prob of A and B among the 5 = 10/21
To find the probability that chips A and B are selected, we need to determine the total number of possible outcomes and the number of favorable outcomes where both chips A and B are selected.
Step 1: Determine the total number of possible outcomes.
Since there are seven chips in the jar and five chips are drawn, the total number of possible outcomes is given by the combination formula:
Total outcomes = nCr(total chips, drawn chips)
= 7C5
= 7! / (5! * (7-5)!)
= 7! / (5! * 2!)
= (7 * 6 * 5!) / (5! * 2)
= (7 * 6) / 2
= 21
Step 2: Determine the number of favorable outcomes.
Since we want chips A and B to be selected, we select them first and then choose the remaining three chips from the remaining five.
The number of ways to select chips A and B is 1 (since we want both chips A and B).
The number of ways to select the remaining three chips from the remaining five is given by the combination formula:
Remaining chips = nCr(total chips - favorable chips, drawn chips - favorable chips)
= 5C3
= 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2)
= (5 * 4) / 2
= 10
Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
Probability = favorable outcomes / total outcomes
= 1 / 21
= 1/21
Therefore, the probability that chips A and B are selected is 1/21.
To find the probability that chips A and B are selected, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
We are drawing 5 chips out of 7, which means 7 chips in the jar and we are choosing 5 of them. This can be calculated using the combination formula C(n, r), where n is the total number of items and r is the number of items chosen. In this case, n = 7 and r = 5.
So, the total number of possible outcomes is C(7, 5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = (7 * 6) / (2 * 1) = 21.
Number of favorable outcomes:
Since we want both chips A and B to be selected, we need to choose 3 more chips out of the remaining 5 chips (C, D, E, F, G). The number of ways to choose 3 chips out of 5 is given by C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10.
Therefore, the number of favorable outcomes is 10.
Probability:
Probability is defined as the number of favorable outcomes divided by the number of possible outcomes.
So, the probability of selecting chips A and B is 10/21.
Thus, the probability that chips A and B are selected is 10/21, or approximately 0.4762.