Choose an American driver at random and let the random variable X be the number of speeding tickets the driver has received in the last two years. The discrete probability distribution of X is shown.

Tickets 0 1 2 3 4 5
Probability 0.16 0.35 0.27 0.10 0.08 0.04

a) Explain in words what the probability P(X≤2) means. What is the probability P(X≤2)?


(b) Write the mathematical expression of the event that a randomly chosen driver has more than three speeding tickets in terms of the random variable X. What is the probability of this event?

Choose an American driver at random and let the random variable X be the number of speeding tickets the driver has received in the last two years. The discrete probability distribution of X is shown.

Tickets 0 1 2 3 4 5
Probability 0.16 0.35 0.27 0.10 0.08 0.04


a) Explain in words what the probability P(X≤2) means. What is the probability P(X≤2)?

P(x\leq 2): what is the probability a randomly chosen driver has no more than 2 tickets? What are the sum of the probabilities corresponding to 0,1, and 2 tickets?



(b) Write the mathematical expression of the event that a randomly chosen driver has more than three speeding tickets in terms of the random variable X. What is the probability of this event?

The expression is like the one in part a, only for more than 3. Add up the probabilities corresponding to having more than 3 tickets. That is, add up the probabilities for 4 and 5 tickets.