Suppose a batsman can hit the ball 50% of the time. If the batsman is given 3 attempts at hitting the ball, what is the probability the batsman will hit the target all three times

A student is taking a true/false exam with 18 questions. If he guesses on each question, what is the probability he will get at least 16 questions correct?

A drunken pirate stands in the center of a ship's deck. Every second the pirate moves right or left only. Every second the pirate moves to the right with a probability of 0.1 The steps are independent of each other. The edge of the deck is 5 steps away from the pirate. What is the chance that the pirate will fall off the ship after exactly 5 seconds?

A basketball player hits three-point shots 45% of the time.  If she takes 4 shots during the game, what is the probability that she misses the first shot and hits the last three shots?

If two fair dice are​ rolled, find the probability that the sum of the dice is 5​,given that the sum is greater than 3.

A software engineer receives a notification anytime a customer sends a crash report. Suppose the software crashes 2% of the time and there are 80 customers who use the software daily. What is the probability that the software engineer receives zero crash reports on any given day?

Two dice are rolled and someone indicates that the two numbers that come up are different. Find the probability that the sum of the two numbers is 8.

A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of at least 3 misses?

For a roll of three dice, show that both a 9 and a 10 can be achieved in six different ways. Nevertheless, show that the probability of rolling a 10 is greater than the probability of rolling a 9.

Please show your solution. A petroleum company exploring for oil has decided to drill 2 wells, one after the other. The probability of not striking oil in the first well is 0.25. Given that they strike oil in the first attempt, the probability of striking oil in the second attempt is 0. 85. What is the probabilty of striking oil in both wells?