Answer:
a. 0.6^x
b. 0.3376
c. 0.6624
d. 2 boxes
Step-by-step explanation:
probability that the selected box of cereal has a prize (P)is 0.4
probability that the selected box of cereal has no prize(p') is 1-0.4 = 0.6
a. probability that you purchase x boxes that do not have the desired prize
= 0.6 *0.6 *0.6 *....up to the x times
=0.6^x
(b) probability that four boxes are purchased =
[tex]P^{4} + P^{3} *Q + P^{2} *Q ^{2} + P *Q^{3} + Q^{4} \\\\= 0.4x^{4} + 0.4^{3} *0.6 + 0.4^{2} *0.6^{2} + 0.4 *0.6^{3} + 0.6^4\\\\ =0.3376[/tex]
(c) probability that you purchase at most four boxes
=1 - probability that four boxes are purchased
= 1- 0.3376 = 0.6624
(d) The desired prize do you expect to purchase:
[tex]=\frac{Q}{1-Q} \\=\frac{0.6}{1-0.6} \\\\=\frac{0.6}{0.4} \\\\= 1.5[/tex]
≈2 boxes
