Question

this data represents the responses of 200 community college students. the variable is \the number of credit cards\ the students had. what is the probability that a student has at least one credit card?

number of credit cards	0	1	2	3	4	5

0.39
0.20
0.61
0.80

what is the probability that a student has at most 4 credit cards?

0.96
0.04
0.97
0.01

Explanation:

Step1: Define the complementary event

The event of having at least one credit - card is the complement of having 0 credit - cards. Let \(P(X\geq1)\) be the probability of having at least one credit - card and \(P(X = 0)\) be the probability of having 0 credit - cards.

Step2: Use the complement rule

The complement rule states that \(P(A)=1 - P(\text{not }A)\). Here, \(P(X\geq1)=1 - P(X = 0)\). Given \(P(X = 0)=0.61\), then \(P(X\geq1)=1 - 0.61=0.39\).

Step3: For the second part, define the event

The event of having at most 4 credit - cards is the complement of having 5 credit - cards. Let \(P(X\leq4)\) be the probability of having at most 4 credit - cards and \(P(X = 5)\) be the probability of having 5 credit - cards.

Step4: Use the complement rule again

By the complement rule, \(P(X\leq4)=1 - P(X = 5)\). Given \(P(X = 5)=0.03\), then \(P(X\leq4)=1 - 0.03 = 0.97\).

Answer:

First question: A. 0.39
Second question: C. 0.97