Answer:
The probability that Karen has bought at least one dented can is 82.5%
Step-by-step explanation:
To know the probability of Karen buying at least one dented can, it's easier to calculate the probability of her not buying any dented can, and we know that:
[tex]P_{\mbox{buying 24 cans}} =P_{\mbox{buying 24 non-dented cans}}+P_{\mbox{at least one dented can}}=1[/tex]
The probability of a can not being dented is (in the same principle as above, 100%(all cans)-7%(dented cans)=93%(non-dented cans) 0.93.
As the probability of a can being dented or not is independent from each other, we multiply the probabilities:
[tex]P_{\mbox{buying 24 non-dented cans}}=0.93^{24}=0.175[/tex]
Now, we calculate the probability of at least one dented can, expressed as a percentage:
[tex]P_{\mbox{at least one dented can}}= (1-P_{\mbox{buying 24 non-dented cans}})*100\\\\P_{\mbox{at least one dented can}}=(1-0.175)*100=82.5\%[/tex]
