20 relay teams took part in the competition - Leaving Cert Mathematics - Question c - 2022

To solve this, we first need to find the individual probabilities for 0, 1, and 2 teams dropping the baton using the binomial formula:

P(k) = {n rack k} p^k (1-p)^{n-k}

where:

• $n = 20$ (the number of teams)
• $p = 0.1$ (the probability of a team dropping the baton)
• $1 - p = 0.9$ (the probability of a team not dropping the baton)

1. Calculate P(0): = 0.12157665459056935$$
2. Calculate P(1): = 0.2707761179692164$$
3. Calculate P(2): = 0.28415504643208866$$

Now, summing these:

= 0.67650881899187441$$ Thus, the final answer rounded to four decimal places is: $$P(at ext{ most } 2) = 0.6765$$