An Experiment consists of flipping a fair coin once and rolling a fair die once. what is the probability of observing a hear or six?
head or a six?
Pr(head or six)= 1-Pr(tail and not a six)
= 1/2*5/6=5/12
Grrrr. I forgot the 1
Pr (head or six)=1=5/12=7/12
In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If the number of spots showing is six, you win $4. And if the number of spots showing is one, two, or three, you win nothing. You are going to play game twice.
The probability that you win $4 both times is
a)1/6
b)1/3
c)1/36
d)1/4
e)1/12
1/4
To find the probability of observing a heads or a six in this experiment, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
1. Total number of possible outcomes:
When flipping a fair coin once, there are 2 possible outcomes: heads (H) or tails (T). When rolling a fair die once, there are 6 possible outcomes: 1, 2, 3, 4, 5, or 6. Since each event is independent, the total number of possible outcomes for both events is given by the product of their respective outcomes: 2 (coin outcomes) * 6 (die outcomes) = 12.
2. Number of favorable outcomes:
We are interested in observing a heads (H) or a six (6). There are two favorable outcomes for the coin (H or T) and one favorable outcome for the die (6). Again, since each event is independent, the number of favorable outcomes for both events is given by the product of their respective outcomes: 2 (coin outcomes) * 1 (die outcome) = 2.
3. Probability calculation:
The probability of an event is defined as the ratio of the number of favorable outcomes to the number of possible outcomes. In this case, the probability of observing a heads or a six is given by the equation:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 2 (favorable outcomes) / 12 (possible outcomes)
Simplifying the fraction, we get:
Probability = 1/6
Therefore, the probability of observing a heads or a six in this experiment is 1/6.