Question

You flip a coin five times and then roll a six sided die

Answer 1

The probability of flipping a coin 5 times and getting heads each time, combined with rolling a fair six-sided die 3 times and getting an even number each time, is 0.0039 or 1/256.

The probability of getting heads on a fair coin flip is 0.5 (1 out of 2 outcomes). Similarly, the probability of rolling an even number on a fair six-sided die is 0.5 (3 even numbers out of 6 total). Since the events are independent, the probability of both events occurring is the product of their individual probabilities.

Probability of getting heads 5 times:
`\(0.5^5\)`

Probability of rolling an even number 3 times:
`\(0.5^3\)`

Multiplying these probabilities:

`\[0.5^5 * 0.5^3 = 0.5^8\]`

Therefore, the overall probability is
`\(0.5^8\)`, which is 1/256 or approximately 0.0039.

The complete question is:
You flip a coin 5 times and then roll a fair six-sided die three times. The coin lands heads up every time and the die shows an even number every time. What’s the probability?