Two children play a simple game with a fair 6-sided die and a coin. During their
ID: 3367679 • Letter: T
Question
Two children play a simple game with a fair 6-sided die and a coin. During their turn, one of the players rolls the die and flips the coin. If the coin comes up tails, then the player's score is the number shown on the die. If the coin comes up heads, then the player's score is triple the number shown on the die. x P(X) Let the random variable X = the points a player scores on their turn. The table for the probability distribution at the right is halfway completed, listing all possible point outcomes (that is, potential X values). 12 15 18 Complete the probability distribution table. Give probabilities to 4 decimal places. (Hint: To compute the probabilities, you may wish to use a tree diagram.)Explanation / Answer
P[X=1] = P[tail appears and 1 comes out from dice]
= P[tail appears | 1 comes out from dice] * P[1 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=2] = P[tail appears and 2 comes out from dice]
= P[tail appears | 2 comes out from dice] * P[2 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=3] = P[tail appears and 3 comes out from dice] + P[head appears and 1 comes out from dice]
= P[tail appears | 3 comes out from dice] * P[3 comes out from dice] + P[head appears | 1 comes out from dice] * P[1 comes out from dice]
= 1/2 * 1/6 + 1/2 * 1/6 = 1/6
P[X=4] = P[tail appears and 4 comes out from dice]
= P[tail appears | 4 comes out from dice] * P[4 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=5] = P[tail appears and 5 comes out from dice]
= P[tail appears | 5 comes out from dice] * P[5 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=6] = P[tail appears and 6 comes out from dice] + P[head appears and 2 comes out from dice]
= P[tail appears | 6 comes out from dice] * P[6 comes out from dice] + P[head appears | 2 comes out from dice] * P[2 comes out from dice]
= 1/2 * 1/6 + 1/2 * 1/6 = 1/6
P[X=9] = P[head appears and 3 comes out from dice]
= P[head appears | 3 comes out from dice] * P[3 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=12] = P[head appears and 4 comes out from dice]
= P[head appears | 4 comes out from dice] * P[4 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=15] = P[head appears and 5 comes out from dice]
= P[head appears | 5 comes out from dice] * P[5 comes out from dice]
= 1/2 * 1/6 = 1/12
P[X=18] = P[head appears and 6 comes out from dice]
= P[head appears | 6 comes out from dice] * P[6 comes out from dice]
= 1/2 * 1/6 = 1/12
So, table becomes,
X P(X) 1 0.08 2 0.08 3 0.17 4 0.08 5 0.08 6 0.17 9 0.08 12 0.08 15 0.08 18 0.08 Total 1.00Related Questions
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