Answer:
Explanation:
The random variable representing the number of heads when a coin is tossed three times can take on values from 0 to 3. To find the probability distribution, we need to determine the probability of each outcome.
Let's start by listing all the possible outcomes:
{hhh, hht, hth, thh, htt, tht, tth, ttt}
The number of heads for each outcome is:
hhh (3 heads)
hht (2 heads)
hth (2 heads)
thh (2 heads)
htt (1 head)
tht (1 head)
tth (1 head)
ttt (0 heads)
Next, let's count the number of outcomes that have each possible number of heads:
0 heads: ttt (1 outcome)
1 head: htt, tht, tth (3 outcomes)
2 heads: hht, hth, thh (3 outcomes)
3 heads: hhh (1 outcome)
Now, we can calculate the probability of each outcome by dividing the number of outcomes with a specific number of heads by the total number of outcomes.
0 heads: 1/8 = 0.125
1 head: 3/8 = 0.375
2 heads: 3/8 = 0.375
3 heads: 1/8 = 0.125
Finally, we can create a graph of the probability distribution for the random variable representing the number of heads. We can use a bar graph where the x-axis represents the number of heads (0, 1, 2, 3) and the y-axis represents the probability.
The graph would look like this:
Number of Heads | Probability
----------------|-----------
0 | 0.125
1 | 0.375
2 | 0.375
3 | 0.125
This graph visually represents the probability distribution for the random variable representing the number of heads when a coin is tossed three times.