the probabilities of a boy passing English and Mathematics tests are x and y. What is the probability of failing both tests(a)1-(x-y)+xy(b)1-(x+y)-xy(c)1-(x+y)+xy(d)1-(x-y)-xy
1-(x+y)+xy
Solution.
P(pass English)= a
P(pass Maths)=b
P(Both pass)= (1+a)(1+b)
P(Both fail)=(1-a)(1-b)
=1 -b-a+ ab
=1-(b+a)+ab
To find the probability of failing both tests, we need to consider the probabilities of passing each test.
Let's break down the problem step by step:
1. The probability of passing the English test is given as 'x'.
2. The probability of passing the Mathematics test is given as 'y'.
Now, we can determine the probability of failing each test:
1. The probability of failing the English test is equal to (1 - x). This is because if the probability of passing is 'x', then the probability of failing is (1 - x).
2. Similarly, the probability of failing the Mathematics test is (1 - y).
Since failing both tests means failing the English test AND failing the Mathematics test, we multiply the probabilities:
Probability of failing both tests = (1 - x) * (1 - y)
Now we can simplify this expression:
Probability of failing both tests = 1 - x - y + xy
So, the correct option is (c) 1 - (x + y) + xy.