Question

In a game of rolling a die. If the number showing is even, you win $3, if the number showing is 1 you win $3 and if the number showing is either 3 or 5 you win nothing. Let x be the amount you win,

i. list the probability distribution of x.

ii. What is the amount of dollar you expect to win?

Answer 1

Answer:

(a)

$\left|\begin{array}{c|c|c}---&---&---\\x&\ 0&\ 3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|$

(b)$2

Step-by-step explanation:

In the given game of rolling a die. these are the possible winnings.

• If the number showing is even(2, 4, or 6) or 1, you win $3.
• If the number showing is either 3 or 5 you win $0.

There are 6 sides in the die.

$P( obtaining a 1,2,4 or 6)=\dfrac46=\dfrac23\\P( obtaining a 3 or 5)=\dfrac26=\dfrac13$

(i)The probability distribution of x.

Let x be the amount won

Therefore:

Probability distribution of x.

$\left|\begin{array}{c|c|c}---&---&---\\x&\ 0&\ 3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|$

(ii) Expected amount of dollar won

Expected Amount

$=\sum x_iP(x_i)\\=(0*\dfrac13)+(3*\dfrac23)\\=\ 2$

You would expect to win $2.