Obtain the Probability Distribution of the Random Variable $\mathrm { X }$

question 158

Multiple Choice

Obtain the probability distribution of the random variable.
-When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Let $\mathrm { X }$ denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

• A)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 0 & 1 / 16 \\
• 1 & 1 / 8 \\
• 2 & 3 / 8 \\
• 3 & 1 / 8 \\
• 4 & 1 / 16
• \end{array}\)
• B)
• \(\begin{array}{l|r}
• x & P(X=x) \\
• \hline 0 & 1 / 16 \\
• 1 & 3 / 16 \\
• 2 & 1 / 2 \\
• 3 & 3 / 16 \\
• 4 & 1 / 16
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 0 & 1 / 16 \\
• 1 & 1 / 4 \\
• 2 & 3 / 8 \\
• 3 & 1 / 4 \\
• 4 & 1 / 16
• \end{array}\)
• D)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 1 / 4 \\
• 2 & 7 / 16 \\
• 3 & 1 / 4 \\
• 4 & 1 / 16
• \end{array}\)

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