4.57 Spell-checking software. Spell-checking software catches “nonword errors,” which are strings of letters that are not words, as when “the” is typed as “eth.” When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:
| Value of X | 0 | 1 | 2 | 3 | 4 |
| Probability | 0.1 | 0.3 | 0.3 | 0.2 | 0.1 |
(a) Sketch the probability distribution for this random variable.
(b) Write the event “at least one nonword error” in terms of X. What is the probability of this event?
(c) Describe the event X ≤ 3 in words. What is its probability? What is the probability that X < 3?