A box contains 5 discs, numbered 1, 2, 4, 6, 7. William takes 3 discs at random, without replacement, and notes the numbers on the discs.
Find the probability that the numbers on the 3 discs are two even numbers and one odd number.
Solution
There are 3 even numbers (2, 4, 6) and 2 odd numbers (1, 7) in the box.
The total number of ways to choose 3 discs from 5 is given by \(\binom{5}{3} = 10\).
To find the number of favorable outcomes (2 even and 1 odd), we can choose 2 even numbers from 3 and 1 odd number from 2:
\(\binom{3}{2} \times \binom{2}{1} = 3 \times 2 = 6\).
Thus, the probability is:
\(\frac{6}{10} = 0.6\).
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