Final answer:
To find the probability of obtaining a head (P(H)) and a tail (P(T)), we divide the number of spins that showed a head or tail by the total number of spins. Using a tree diagram, we can find the probabilities of each possible outcome for spinning the coin twice. The probability of obtaining exactly one head in two spins of the coin is found by adding up the probabilities of the outcomes that have one head. The probability of obtaining at least one head is found by subtracting the probability of no heads from 1.
Step-by-step explanation:
a. To find the probability of obtaining a head (P(H)), we divide the number of spins that showed a head (140) by the total number of spins (250). So, P(H) = 140/250 = 0.56.
To find the probability of obtaining a tail (P(T)), we divide the number of spins that showed a tail (110) by the total number of spins (250). So, P(T) = 110/250 = 0.44.
b. To find the probabilities of each possible outcome for spinning the coin twice, we can create a tree diagram. Starting with the first spin, each branch will represent the possible outcomes (H or T), and the probabilities will be based on the given probabilities (P(H) = 0.56, P(T) = 0.44). In the second spin, we continue the branches for each possible outcome in the first spin and multiply the probabilities. For example, the probability of getting HH is P(H) * P(H) = 0.56 * 0.56 = 0.3136.
c. To find the probability of obtaining exactly one head in two spins of the coin, we add up the probabilities of the outcomes that have one head. So, P(exactly one head) = P(HT) + P(TH) = 0.56 * 0.44 + 0.44 * 0.56 = 0.2464 + 0.2464 = 0.4928.
d. To find the probability of obtaining at least one head, we add up the probabilities of all the outcomes that have at least one head. So, P(at least one head) = 1 - P(no heads) = 1 - P(TT) = 1 - P(T) * P(T) = 1 - 0.44 * 0.44 = 1 - 0.1936 = 0.8064.