For a sales promotion, the manufacturer places winning symbols under the caps of 23% of all its soda bottles. If you buy a six-pack of soda, what is the probability that you win something?

1 answer

Question:

For a sales promotion, the manufacturer places winning symbols under the caps of 23% of all its soda bottles. If you buy a six-pack of soda, what is the probability that you win something?

Answer:The probability that you win something is 0.7916.Step-by-step explanation:Let X denote the number of soda bottles having winning symbols under the caps.The proportion of soda bottles having winning symbols under the caps is, p = 0.23.Six-pack of soda are randomly bought.Every bottle is independent of the others to have the symbols under the caps.The random variable X follows a binomial distribution with parameters n = 6 and p = 0.23.Then the chance of winning something implies that at least 1 of the bottles in the six-pack have the symbol under the caps.Compute the value of P (X ≥ 1) as follows: [tex]P(X\geq 1)=1-P(X<1)\\\\=1-P(X=0)\\\\=1-{6\choose 0}(0.23)^{0}(1-0.23)^{6-0}\\\\=1-0.2084224\\\\=0.7915776\\\\\approx 0.7916[/tex]Thus, the probability that you win something is 0.7916.

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