Question

a fair coin is flipped three times. the sample space for this experiment is as follows: {hhh, hht, hth, htt, thh, tht, tth, ttt} which table represents the experiment and the probabilities for number of heads? table a

number of heads, x	p(x)
1	1/8
2	1/8
3	3/8

Explanation:

Step1: Count total outcomes

The sample - space has 8 elements: $\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$, so the total number of outcomes $n = 8$.

Step2: Calculate probability for 0 heads

The outcome with 0 heads is $TTT$, so $n(0)=1$. The probability $P(0)=\frac{n(0)}{n}=\frac{1}{8}$.

Step3: Calculate probability for 1 head

The outcomes with 1 head are $HTT, THT, TTH$, so $n(1) = 3$. The probability $P(1)=\frac{n(1)}{n}=\frac{3}{8}$.

Step4: Calculate probability for 2 heads

The outcomes with 2 heads are $HHT, HTH, THH$, so $n(2)=3$. The probability $P(2)=\frac{n(2)}{n}=\frac{3}{8}$.

Step5: Calculate probability for 3 heads

The outcome with 3 heads is $HHH$, so $n(3)=1$. The probability $P(3)=\frac{n(3)}{n}=\frac{1}{8}$.

Answer:

The correct table should be:

Number of Heads, $x$	$P(x)$
1	$\frac{3}{8}$
2	$\frac{3}{8}$
3	$\frac{1}{8}$

So the given Table A is incorrect.