Explanation:
The correct answer is C.
P (5) = P (5/T) * P (T) + P (5/H) * P (H)
P (5) = (1/9) * (1/2) + (1/6) * (1/2) = 5/36
P (T/5) = P (5/T) * P (T)/P (5)
P (T/5) = (1/9) * (1/2)/(5/36) = 2/5
Further explanation: The probability P(5/H) is a conditional probability, indicating that the player has already flipped the coin and obtained a head (H). Given this information, the player only rolls the dice once, as the coin is showing a head. It's important to note that rolling a dice has six possible outcomes (1, 2, 3, 4, 5, 6), each with an equal probability of 1/6. Therefore, the probability of the player rolling the dice and obtaining a 5 is 1/6. The question states that if the coin turns up tails, the player will roll two dice. In this case, the player will have a sample size of 36 (6 outcomes for the first dice multiplied by 6 outcomes for he second dice). The question further specifies that the player moves 5 times. If the coin turns out to be tails, the possible outcomes are (1,4), (2,3), (3,2), and (4,1) out of the total sample space of 36 outcomes. Therefore, the probability P(5|T) is calculated as 4/36, which simplifies to 1/9.
Ultimate access to all questions.
In a game, a coin is flipped. If the coin is heads, the player rolls one die. If the coin turns up tails, the player rolls two dice and the player moves their playing piece the number of spots shown on the die or dice. Given that on a player's turn, he moves 5 spaces, what is the probability he flipped tails on the coin?
A
1/10
B
1/5
C
2/5
D
1/3
