Question

s2 l3 3. determine if events a and b are mutually exclusive. * p(a)=\frac{3}{10} p(b)=\frac{1}{4} p(a or b)=\frac{23}{50} mutually exclusive not mutually exclusive

Explanation:

Step1: Recall the formula for mutually - exclusive events

For mutually exclusive events \(A\) and \(B\), \(P(A\ or\ B)=P(A)+P(B)\).

Step2: Calculate \(P(A)+P(B)\)

Given \(P(A)=\frac{3}{10}\) and \(P(B)=\frac{1}{4}\). First, find a common denominator. The common denominator of 10 and 4 is 20. So \(P(A)=\frac{3\times2}{10\times2}=\frac{6}{20}\) and \(P(B)=\frac{1\times5}{4\times5}=\frac{5}{20}\). Then \(P(A)+P(B)=\frac{6 + 5}{20}=\frac{11}{20}=\frac{27.5}{50}\).

Step3: Compare with \(P(A\ or\ B)\)

Given \(P(A\ or\ B)=\frac{23}{50}\). Since \(\frac{23}{50}
eq\frac{27.5}{50}\) (i.e., \(P(A\ or\ B)
eq P(A)+P(B)\)), events \(A\) and \(B\) are not mutually exclusive.

Answer:

Not Mutually Exclusive