Match the following statements as to whether it is a Theoret

Match the following statements as to whether it is a Theoretical Probability or an Empirical Probability. Two dice are rolled 100 times and it was found that 2-heads showed up 25 times. Thus the probability of flipping two heads is 1/4 Answer 1.... Selecting a King from a standard deck of cards has a probably of 4/52=1/13. Answer 2.... A hospital has found that 157 patients arrived with cardiac arrests and of these 21 died within the week. Thus the probability of dying from a heart attack is 21/157 Answer 3.... The probability of selecting a red rock out of a bag that contains 5 red rocks and 12 blue rocks is 5/17. Answer 4... The Buck\'s have a 2/5 chance to win the game

Solution

A statement relates to Empirical Probability when the probability is calculated using observable events, like 1 in 4 cases were observed to be successful, so probability of success is 1/4.

A statement refers to Theoretical Probability when the probability is calculated using known knowledge and without the use of any observation, like 3 bags are red and 1 bag is blue, so probability a randomly selected bag is red is 3/4.

So,

Answer 1: Empirical Probability : As it was observed that 2 heads showed up 25 times out of 100.

Answer 2: Theoretical Probability: As it is known that there are 4 kings in 52 cards.

Answer 3: Empirical Probability : As it was observed that 21 died out of 157 patients.

Answer 4: Theoretical Probability: As it is known that there are 5 red rocks out of 17 rocks.

Answer 5: Theoretical Probability: As game has not yet happened and it is an estimation from known knowledge.