Write the probability distribution when three coins are tossed.
- $X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$
- $X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 7 }{ 8 } \end{matrix}$
- $X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 7 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$
- $X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$
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A
Correct answer
Explanation
For 3 coins, the outcomes are 0 heads (1), 1 head (3), 2 heads (3), 3 heads (1) out of 8 total. The probability distribution is 1/8, 3/8, 3/8, 1/8.
AI explanation
When three coins are tossed, the total number of possible outcomes is 2 cubed, which equals 8. Using the binomial distribution formula, the probability of getting exactly X heads is given by the combination of 3 items chosen X at a time, multiplied by 1/2 cubed. For X equals 0, 1, 2, and 3, the combinations are 1, 3, 3, and 1, resulting in probabilities of 1/8, 3/8, 3/8, and 1/8, respectively.