Step-by-step explanation:
Theoretical probability is the probability we expect or calculate.
Experimental probability is the probability we measure or observe.
1. The theoretical probability of two heads showing is:
P(2 heads) = P(head) × P(head)
P(2 heads) = 0.5 × 0.5
P(2 heads) = 0.25
2. The experimental probability of two heads showing is:
P(2 heads) = 26 / 100
P(2 heads) = 0.26
3. The theoretical probability of two tails showing is:
P(2 tails) = P(tail) × P(tail)
P(2 tails) = 0.5 × 0.5
P(2 tails) = 0.25
4. The experimental probability of two tails showing is:
P(2 tails) = 25 / 100
P(2 tails) = 0.25
5. The theoretical probability of one head and one tail is:
P(head and tail) = P(head, then tail) + P(tail, then head)
P(head and tail) = 0.5 × 0.5 + 0.5 × 0.5
P(head and tail) = 0.25 + 0.25
P(head and tail) = 0.5
6. The experimental probability of one head and one tail is:
P(head and tail) = 49 / 100
P(head and tail) = 0.49
7. The differences between the theoretical and experimental probabilities may simply be because there's a finite number of coin tosses, and each coin toss is independent of each other.