a bag consist of 4 red, 5 blue and 6 green coloured socks. if 3 socks are selected, what is the probability that exact one of them is blue?
To find the probability of selecting exactly one blue sock out of three, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When selecting three socks, the total number of outcomes is given by the combination formula (nCr), where n is the total number of socks in the bag and r is the number of socks to be selected. In this case, we have 15 socks in total (4 red + 5 blue + 6 green).
Number of Favorable Outcomes:
To have exactly one blue sock, we can select one blue sock and two socks of any other color. The number of ways to do this is calculated as follows:
Number of ways to choose one blue sock = 5C1
Number of ways to choose two socks of any other color = (4+6)C2
Thus, the number of favorable outcomes is (5C1) * ((4+6)C2).
Probability Calculation:
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Let’s calculate the probability:
Number of favorable outcomes = (5C1) * ((4+6)C2) = 5 * 45 = 225
Total number of outcomes = 15C3 = 455
Probability = 225 / 455 = 0.4945 (rounded to four decimal places)
Therefore, the probability that exactly one of the three selected socks is blue in the given bag is approximately 0.4945 or 49.45%.