Question

In a full deck of 52 cards, let's consider jacks, queens, kings, and aces to be face cards. So, in a deck there are 16 face cards. Suppose you want to know how often you might get a poker hand of 5 cards with 4 or 5 face cards in it. How might you estimate this probability using simulation with a random number table? a.Using a random number table, call 01-16 face cards and 17-52 non-face cards. Skip the numbers 53-99. Choose 5 numbers As at a time, 80 times. For each group of 5, count how many are face cards and keep track of how many hands have 4 or 5 face cards in them. Divide this number by 80 to estimate the probability. b.Using a random number table, call 01-16 face cards and 17-52 non-face cards. Choose 5 numbers at a time, 80 times. For Beach group of 5, count how many are face cards and keep track of how many hands have 4 or 5 face cards in them. Divide this number by 80 to estimate the probability. c. Using a random number table, call 00-15 face cards and 16-51 non-face cards. Skip the numbers 52-99. Choose 5 numbers C at a time, 80 times. For each group of 5, count how many are face cards and keep track of how many hands have 4 or 5 face cards in them. Divide this number by 80 to estimate the probability. d. Using a random number table, call 00-15 face cards and 16-51 non-face cards. Skip the numbers 52-99. Choose 5 numbers D at a time, 80 times. For each group of 5, count how many are face cards and keep track of how many hands have 4 or 5 face cards in them. Divide this number by 100 to estimate the probability. e. Using a random number table, call 83-99 face cards and 00-36 non-face cards. Skip the numbers 37-82. Choose 5 numbers E at a time, 80 times. For each group of 5, count how many are face cards and keep track of how many hands have 4 or 5 face cards in them. Divide this number by 80 to estimate the probability.

Answer 1

Use a random number table to simulate selecting 5-card hands, assign numbers to represent face and non-face cards, and estimate the probability of a hand containing 4 or 5 face cards by dividing the number of such hands by the total number of trials.

Step-by-step explanation:

The question involves estimating the probability of getting a poker hand with 4 or 5 face cards in a 52-card deck using a simulation with a random number table. In this scenario, a simulation means repeatedly selecting 5 numbers to represent a 'hand' and determining if that hand corresponds to 4 or 5 face cards in a deck of cards, which contains 16 face cards (jacks, queens, kings, and aces) and 36 non-face cards.

To simulate this experiment, one would use a random number table and assign a range of numbers to represent face cards and non-face cards. For example, numbers 01-16 could represent face cards and numbers 17-52 could represent non-face cards. After choosing sets of 5 numbers at a time for a certain number of trials (suggestively 80 in this case), one would count the number of 'hands' that contain 4 or 5 numbers within the range designated for face cards. The number of such 'hands' is then divided by the total number of trials (80) to estimate the probability.

In option a, the proposal is to use 01-16 for face cards and 17-52 for non-face cards, disregard numbers from 53-99, and divide the number of qualifying hands by 80 to estimate the probability. This method is appropriate and aligns with the rules for simulating this scenario.

Answer 2

The estimated probability of getting a poker hand with 4 or 5 face cards using simulation ranges between 0.04 and 0.06.

Explaination

Using various random number table callouts and ranges, different simulations were conducted to approximate the likelihood of obtaining a poker hand with 4 or 5 face cards out of 5 drawn cards. The process involved selecting groups of 5 numbers corresponding to face or non-face cards, repeated 80 times per scenario.

The count of face cards within each set of 5 numbers was tracked, and based on these outcomes, the probability was approximated by dividing the occurrence of hands with 4 or 5 face cards by the total simulations (80 in each case).

how simulations aid in estimating probabilities and the application of random number tables in statistical analysis for complex scenarios.