the probabilty that a person will solve aproblem is 1/5. what is the probabily that he solves at least one problem out of ten problems

To solve this problem, we can use the concept of complementary probability.

Step 1: Understand the problem The probability that a person will solve a problem is 1/5. We want to find the probability that the person solves at least one problem out of ten.

Step 2: Complementary probability The complementary probability of a person solving a problem is the probability that the person does not solve the problem. This is calculated as 1 - the probability of the person solving the problem. So, the complementary probability is 1 - 1/5 = 4/5.

Step 3: Probability of not solving any problem out of ten The probability that the person does not solve any problem out of ten is (4/5)^10.

Step 4: Probability of solving at least one problem out of ten The probability that the person solves at least one problem out of ten is the complement of the probability that the person does not solve any problem out of ten. So, the probability is 1 - (4/5)^10.

So, the probability that the person solves at least one problem out of ten is 1 - (4/5)^10.