Question

a student must choose to participate in two different events during field day. there are four track events, two academic events, and six team sports events. what is the approximate probability that the student will choose to participate in two team sports? 0.114 0.227 0.273

Explanation:

Step1: Calculate total number of events

The total number of events is \(4 + 2+6=12\).

Step2: Calculate number of ways to choose 2 - event combinations

The number of ways to choose 2 events out of 12 is given by the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 12\) and \(r = 2\). So \(C(12,2)=\frac{12!}{2!(12 - 2)!}=\frac{12\times11}{2\times1}=66\).

Step3: Calculate number of ways to choose 2 team - sports events

The number of ways to choose 2 team - sports events out of 6 is \(C(6,2)=\frac{6!}{2!(6 - 2)!}=\frac{6\times5}{2\times1}=15\).

Step4: Calculate the probability

The probability \(P\) that the student will choose 2 team - sports events is \(P=\frac{C(6,2)}{C(12,2)}=\frac{15}{66}\approx0.227\).

Answer:

0.227