A gambler playing blackjack in a casino using four decks noticed that 20% of the cards that had been dealt were jacks, queens, kings, or aces. After x cards had been dealt, he knew that the likelihood that the next card dealt would be a jack, a queen, a king, or an ace was (64-0.2x)/(208-x) For what values of x is this likelihood greater than 70%? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The number of cards dealt must be more than and less than or equal tc The likelihood that the next card dealt would be a jack, a queen, a king, or an ace can never be greater than 70%.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?