Question

You flip a coin and then roll a fair six-sided die. the coin lands heads-up and the die shows an even number. Are these independant or dependant events? calculate their probablility.​

Answer 1

The events of flipping a coin and rolling a die are independent events. This means that the outcome of one event does not affect the outcome of the other event.

To calculate the probability of both events occurring, we multiply the probabilities of each event together.

The probability of the coin landing heads-up is 1/2, since there are two equally likely outcomes (heads or tails) and only one of them is heads.

The probability of rolling a fair six-sided die and getting an even number is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

To find the probability of both events occurring, we multiply the probabilities: (1/2) * (1/2) = 1/4.

Therefore, the probability of flipping a coin and getting heads, and rolling a die and getting an even number, is 1/4 or 0.25.

Answer 2

The events of flipping a coin and rolling a die are independent events.

To determine the probability of these events, we need to consider the probability of each event separately and then multiply the probabilities together.

1. Probability of getting heads on the coin flip: Since there are two possible outcomes (heads or tails) and the coin is fair, the probability of getting heads is 1/2 or 0.5.

2. Probability of rolling an even number on the six-sided die: Out of the six possible outcomes (numbers 1 to 6), there are three even numbers (2, 4, and 6). So the probability of rolling an even number is 3/6 or 0.5.

Since these events are independent, we can multiply the probabilities together:

Probability = Probability of heads * Probability of even number

Probability = 0.5 * 0.5

Probability = 0.25 or 25%

Therefore, the probability of both events occurring, the coin landing heads-up and the die showing an even number, is 0.25 or 25%.

I hope this helps! Let me know if you have any further questions.