isabelle attended a music stores banjo sale. she counted the types of banjos and made note of their…

isabelle attended a music stores banjo sale. she counted the types of banjos and made note of their discounts. 25% off 50% off 4 strings 4 7 5 strings 3 5 are the events \the banjo has 4 strings\ and \the banjo is 50% off\ independent? yes no submit

Answer

Explanation:

Step1: Calculate total number of banjos

$4 + 7+3 + 5=19$

Step2: Calculate probability of a banjo having 4 - strings

$P(4 - strings)=\frac{4 + 7}{19}=\frac{11}{19}$

Step3: Calculate probability of a banjo having 50% off

$P(50% - off)=\frac{7 + 5}{19}=\frac{12}{19}$

Step4: Calculate probability of a banjo having 4 - strings and 50% off

$P(4 - strings\ and\ 50% - off)=\frac{7}{19}$

Step5: Check independence condition

If two events $A$ and $B$ are independent, then $P(A\ and\ B)=P(A)\times P(B)$. $P(4 - strings)\times P(50% - off)=\frac{11}{19}\times\frac{12}{19}=\frac{132}{361}\approx0.366$ $P(4 - strings\ and\ 50% - off)=\frac{7}{19}\approx0.368$ Since $\frac{132}{361}\neq\frac{7}{19}$, the events are not independent.