In a quiz program, 3 questions on sprots, 3 questions on general knowledge, and 4 questions on science are printed separately on 10 cards and placed upside down. John is asked to select 2 cards at random. What is the probability of Joohn selecting 2 questions on science?
Number of ways to select any two of the 10
= C(10,2) = 45
number of ways to select 2 out of the science
= C(4,2) = 6
prob of that event = 6/45 = 2/15
To find the probability of John selecting 2 questions on science, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways John can choose 2 cards out of the 10 cards, which can be calculated using the combination formula:
nCr = n! / [(n-r)! * r!]
In this case, n = 10 (total number of cards) and r = 2 (number of cards John needs to choose). Plugging in these values, we get:
10C2 = 10! / [(10-2)! * 2!] = 45
So, there are 45 possible outcomes.
Now, let's calculate the number of favorable outcomes, or the number of ways John can select 2 questions on science. Out of the 10 cards, there are 4 questions on science. John needs to select 2 cards from this subset (questions on science), which can be calculated as:
4C2 = 4! / [(4-2)! * 2!] = 6
So, there are 6 favorable outcomes.
Finally, we can calculate the probability of John selecting 2 questions on science by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 6/45
= 2/15
Therefore, the probability of John selecting 2 questions on science is 2/15.