Final answer:
A tree diagram can be used to illustrate possible outcomes when flipping 5 coins. The probability of flipping 4 heads can be calculated using the binomial coefficient formula. The probability of flipping either 5 heads or 5 tails can be obtained by adding the probabilities of these two events occurring separately.
Step-by-step explanation:
A tree diagram can be used to illustrate possible outcomes when flipping 5 coins. Each branch represents a possible outcome, either heads (H) or tails (T). Since there are 2 outcomes for each coin flip, and we are flipping 5 coins, the total number of possible outcomes is 2^5 = 32. The tree diagram would have 32 branches.
To calculate the probability of flipping 4 heads, we need to determine how many ways we can get 4 heads out of 5 coin flips. This can be done using the binomial coefficient formula: C(5,4) = 5! / ((5-4)! * 4!). Substituting the values into the formula, we get C(5,4) = 5. So, there are 5 ways to get 4 heads out of 5 coin flips. Since the probability of getting heads on a fair coin flip is 0.5, the probability of flipping 4 heads is (0.5)^4 = 0.0625 or 6.25%.
To calculate the probability of flipping either 5 heads or 5 tails, we add the probabilities of these two events occurring separately. Since each coin flip is an independent event, the probability of getting 5 heads in a row is (0.5)^5 = 0.03125 or 3.125%, and the probability of getting 5 tails in a row is also (0.5)^5 = 0.03125 or 3.125%. Adding these two probabilities gives us a total probability of 6.25% for flipping either 5 heads or 5 tails.