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?

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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

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

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: 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?

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(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?

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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.