Question

This is the typical example for a Bernoulli trial, with 2 possible results of constant probability:

A) Rolling a Six-Sided Die
B) Flipping a Coin
C) Drawing a Card from a Deck
D) Tossing a Football

Answer 1

A Bernoulli trial is an experiment with two possible outcomes and constant probabilities. Examples include rolling a die and tossing a coin. In this case, the sample space is {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}.

Step-by-step explanation:

A Bernoulli trial is an experiment with two possible outcomes, success and failure, where the probability of success is constant for each trial. Examples of Bernoulli trials include flipping a coin, rolling a six-sided die, drawing a card from a deck, and tossing a football (if we assume it has only two possible outcomes).

1. Sample space: The sample space for rolling a die and tossing a coin is {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}.
2. Probability of event A: Event A is the first roll being a three or a four and the coin toss landing on a head. Since there are 12 possible outcomes in the sample space and 2 of them satisfy event A (3H and 4H), the probability of A is P(A) = 2/12 = 1/6.
3. Mutually exclusive events: Events A and B are not mutually exclusive because there can exist outcomes that satisfy both events. Event B is the first and second tosses both landing on heads, which has only one possible outcome (HH). Since there is an outcome (3H) that satisfies both A and B, these events are not mutually exclusive.