 Hi and how are you all today? My name is Priyanka and let us discuss this question. It says x is taking up subjects, mathematics, physics and chemistry in an examination. His probabilities of getting grade A in the subjects are 0.2, 0.3 and 0.5 respectively. Find the probability that he gets grade A in all subjects, grade A in no subjects, grade A in two subjects. So here, suppose the following events b is equal to x receives grade A in mathematics. Let p be x receives grade A in physics and let c be equal to x receives grade A in chemistry. Now, we have probability of m given as 0.2, probability of p given as 0.3 and probability of c given as 0.5. Probability of getting grade A in will be 1 minus 0.2 that is 0.8, same way that is 0.7 and probability not probability of getting grade A in chemistry is 0.5 that is 1 minus 0.5. For the first part, we need to find out probability that he gets grade A in all subjects that is probability of m intersection p intersection c that is the product of their probabilities that is further equal to 0.2 into 0.3 into 0.5 which gives us the answer as 0.0.3. So this is the answer to the first part. With the help of this first part, we can easily find out the probability of getting grade A in no subject that will be 1 minus this probability that is coming out to be 0.0 sorry it will be probability of not getting grade A in maths probability of not getting grade A in physics and probability of not getting grade A in chemistry that is 0.8 into 0.7 into 0.5 that is coming out to be 0.28. So this is the answer to the second part. Now proceeding with the last part. We need to find out probability of getting grade A equal to probability of getting grade A in physics grade A in sorry grade A in maths then physics into probability of getting not a grade A in chemistry or we have other it as probability of getting a grade A in maths not in physics but in chemistry or it can be probability of not getting a grade A in maths but getting grade A in physics and in chemistry. What we need to do is we just need to substitute the value that is 0.8 into 0.3 into 0.5, 0.2 into 0.7 into 0.5 plus 0.8 it will be 0.2 0.8 into 0.3 into 0.5 it comes out to be 0.03 plus 0.12 plus 0.07 that is 0.22 as our answer to the last and final part. Hope you understood it and to take care of your calculations enjoy by for now.