Question

Construct a probability distribution of getting heads in a three-coin toss?

Answer 1

To construct a probability distribution of getting heads in a three-coin toss, we consider all possible outcomes and their probabilities. In a three-coin toss, there are 8 possible outcomes with each having an equal probability of 1/8. Therefore, the probability of getting heads in a three-coin toss is 1/2.

Step-by-step explanation:

To construct a probability distribution of getting heads in a three-coin toss, we need to consider all possible outcomes and their probabilities. In a three-coin toss, there are 2^3 = 8 possible outcomes, as each coin can either land on heads (H) or tails (T). Here is the probability distribution:

Each outcome has an equal probability of 1/8. Therefore, the probability of getting heads in a three-coin toss is 4/8 or 1/2.

Answer 2

To construct a probability distribution for a three-coin toss, list all combinations of heads (H) and tails (T), count the occurrence of heads, and assign probabilities assuming the coin is fair and each toss is independent, resulting in 0 heads (1/8), 1 head (3/8), 2 heads (3/8), and 3 heads (1/8).

Step-by-step explanation:

Probability Distribution for Three-Coin Toss

When tossing a coin three times, the total number of outcomes is 23, which is 8 possible combinations. To construct a probability distribution, we consider each possible outcome of heads (H) and tails (T). Here are the combinations:

• HHH
• HHT
• HTH
• HTT
• THH
• THT
• TTH
• TTT

Next, we count the occurrence of heads in each combination:

• 0 heads: TTT (1 way)
• 1 head: HTT, THT, TTH (3 ways)
• 2 heads: HHT, HTH, THH (3 ways)
• 3 heads: HHH (1 way)

Assuming the coin is fair and each toss is independent, the probability for each number of heads is:

• P(0 heads) = 1/8
• P(1 head) = 3/8
• P(2 heads) = 3/8
• P(3 heads) = 1/8

This is the probability distribution for the number of heads in a three-coin toss.