# probability distribution of X

• May 17th 2006, 07:26 AM
skhan
probability distribution of X
so heres the question
i dont know how to construct a probability distribution of X
the answers are shown below but i dont know how they were obtained

A player tosses a coin. If he obtains a head he is permitted to throw a die and receive, in dollars, the number of points showing on the die. If he obtains a tail he is not permitted to throw the die but he does receive \$2. Let X be the number of dollars that a player can win in one attempt at this game if bith the coin and the die are fair. What is the probability distribution of X?

X {1, 2, 3, 4, 5, 6}
P(X) {0.083, 0.583, 0.083, 0.083, 0.083, 0.083}
• May 18th 2006, 12:22 PM
skhan
i finally got this question!

when u toss a coin you have a 50/50 chance of getting a head or tail and if you get head you roll a die to get either 1, 2, 3, 4, 5, 6, BUT if you get a tail you simply get \$2

COIN --> (0.5 chance) Head --> 1, 2, 3, 4, 5, 6 --> \$1, \$2, \$3, \$4, \$5, \$6
~ 1/6 = 0.166 chance of getting either 1, 2, 3, 4, 5, 6,

--> (0.5 chance) Tail --> \$2

so for X = \$1, you get 0.166 x 0.5 chance of getting a head = 0.08333
for X = 3, 4, 5, 6 it is the same 0.166 x 0.5 to get = 0.08333

but for X = \$2 you have (0.166x0.5) + 0.5 from tail = 0.5833