Question

At the fair is the game of tossing the coin. If Gildardo participates and gives him three coins, what is the probability that Gildardo will make all three coins fall on the same face?

A) 1/2
B) 1/4
C) 1/8
D) 1/16

Answer 1

The probability of Gildardo making all three coins fall on the same face at the fair is the product of the probabilities of each individual toss, with two possible favorable outcomes (all heads or all tails). The calculation is (1/2)^3 = 1/8, which corresponds to option C.

Step-by-step explanation:

The question asks about the probability of Gildardo making all three coins fall on the same face in a coin tossing game. To find this probability, we note that a fair coin has two sides, head (H) and tail (T), and each has an equal chance of landing face up when the coin is tossed. For one coin toss, there are two possible outcomes (H or T), and the probability of either side landing face up is 0.5.

Considering three independent coin tosses, the probability of all three coins landing on the same face is the product of the probabilities of each individual toss. There are two ways this can happen: either all coins land as heads (HHH) or all coins land as tails (TTT). The probability for each separate event is (1/2) x (1/2) x (1/2), since the tosses are independent.

Thus, the probability of all heads or all tails is (1/2)3 for one event, which is 1/8. Since there are two such favorable outcomes, we multiply this by 2, giving us 2 x 1/8 = 1/4. However, since the question specifically asks about them all falling on the same face, we do not need to double count, so the correct answer is (1/2)3 or 1/8, which is option C.