A soccer striker scores on average in one game in five. Find the probabilities that he scores only once out of his next seven games, correcting to three4 decimal places.

Wendy has a 0.35 chance of correctly answering any multiple choice question she attempts.
She is given 20 to attempts. Find the probability that she got at least 1 right, correcting to four decimal places.

A machine manufacturing bolts is known to produce on average one defective bolt per hundred. Find the probability that no defective bolts at all in 10 made, correcting to four decimal places.

A fair coin is tossed five times. Find the probability of obtaining two Heads and three Tails.

A biased coin has a 60% of probability of getting a Tail. This coin is tossed five times. Find the probability of obtaining at least two Tails.

Five per cent of items made by a factory machine are defective. The items are packed and sold in boxes of 20. Find the probability of at least one items being defective in a box, correcting to four decimal places.

A binomial random variable has a mean of 8 and a variance of 6.4. Find \(\Pr \left( {X = 10} \right)\), correcting to four significant figures.

A binomial random variable has a mean of 6 and a variance of 3.6. Find \(\Pr \left( {X = 103} \right)\), correcting to four significant figures.

A binomial experiment is completed 50 times, with the expected number of successes being 15. Find the standard deviation, correcting to three significant figures.

A set of multiple-choice questions with five different choices of answer for each question. If the answers to each question are guessed and the expected number of correct is 8, find the probability of getting 25% of the question correct, correcting to three significant figures.