In an exam, 10 questions of true-false type are asked. A student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers true and if it falls tails, he answers false. Show that the probability that he answers at most 7 questions correctly is `121/128`.

In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true', if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.

In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it is 1/8. Find the probability that he knew the answer to the question, given that he correctly answered it.

In answering a question in a multiple choice test a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 . What is the probability that a student knows the answer, given that he answered it correctly ?

Answer the following question 1G= 10^-4T True or false?

In a multiple choice questions there are four alternative answers, of which one or more correct. A candidate will get marks in the question only if the ticks all the correct answers. The candidate decides to tick answers at random. If the is allowed upto three chances to answer the question, find the probability that he will get marks in the questions.

In a multiple choice question, there are five alternative answers of which one or more than one are correct. A candidate will get marks on the question, if he ticks all the correct answers. If he decides to tick answer all random, then the least number of choices should he be allowed, so that the probability of his getting marks on the question exceeds (1)/(8) is

In the following experiment have equally likely outcomes?Explain. A trial is made to answer a true-false question. The answer is right or wrong.

For a set of five true or false questions, no student has written all correct answers, and no two students have given the same sequence of answers. What is the maximum number of students in the class, for this to be possible ?