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%.

Question

Mathematics

Penelope Glenn

18 June, 06:10

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%.

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Answers (1)

Know the Answer?

Douglas Dudley · Answer 1

x = 162 cards need to be dealt with

Step-by-step explanation:

Given:

- Estimation of likelyhood of next card to be queen, a king, or an ace:

(64 - 0.2*x) / (208 - x)

Find:

For what values of x is this likelihood greater than 70%?

Solution:

- Use the likely-hood estimation relation and set up the inequality as follows:

(64 - 0.2*x) / (208 - x) > 0.7

(64 - 0.2*x) > 0.7 * (208 - x)

64 - 0.2*x > 145.6 - 0.7*x

0.5*x > 81.6

x > 163.2

- It would require 162 cards to be dealt with for the probability of next card being queen, a king, or an ace is greater than 70%