Question

Kim rolls a dice and flips a coin

a) Calculate the probability that she
gets a 2 and a head.
b) Work out the probability that she
gets an even number and a tail.
a)
Probability is

Answer 1

2

Explanation:

a) Calculate the probability that she

b) Work out the probability that she

gets an even number and a tail.

a)

Probability is

Answer 2

a)
`\[ P(\text{2 and Head}) = (1)/(12) \]`\

b)
`\[ P(\text{Even Number and Tail}) = (1)/(4) \]`

a) Probability of Getting a 2 and a Head:

When rolling a six-sided die and flipping a coin, the probability of getting a specific outcome for each event is
`\( (1)/(6) \)` for rolling a 2 and
`\( (1)/(2) \)` for getting a head. Since these events are independent, you multiply the probabilities to find the joint probability:

`\[ P(\text{2 and Head}) = P(\text{2}) * P(\text{Head}) = (1)/(6) * (1)/(2) = (1)/(12) \]`

Therefore, the probability that Kim gets a 2 and a head is
`\( (1)/(12) \)`.

b) Probability of Getting an Even Number and a Tail:

For getting an even number on a six-sided die, there are three favorable outcomes (2, 4, 6) out of six possible outcomes. The probability of getting an even number is
`\( (3)/(6) = (1)/(2) \)`. The probability of getting a tail in a coin flip is
`\( (1)/(2) \)`. Since these events are independent, you multiply the probabilities:

`\[ P(\text{Even Number and Tail}) = P(\text{Even Number}) * P(\text{Tail}) = (1)/(2) * (1)/(2) = (1)/(4) \]`

Therefore, the probability that Kim gets an even number and a tail is
`\( (1)/(4) \).`