Question

Of the boxes of cruncho cereal on a supermarket shelf 25 percent contain a prize and the other 75 percent contain no prize.if Gerry buys two boxes of cruncho cereal which of the following is closest to the probability that neither box contain a prize?
$\frac{7}{10}$
$\frac{9}{16}$
$\frac{3}{4}$
$\frac{15}{16}$


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Answer 1

Answer:

$X \sim Binom(n=2, p=0.25)$

And for this case we want to find the following probability:

$P(X=0)$

And we can use the probability mass function given by:

$P(X) = nCx (p)^x *1-p)^{n-x}$

And replacing we got:

$P(X=0)= (2C0) (0.25)^0 (1-0.25)^{2-0}= 0.5625= \frac{9}{16}$

Step-by-step explanation:

For this problem we can define the random variable of interest X as "the number of bxes with a cereal" and for this problem we can model the variable with the following distribution:

$X \sim Binom(n=2, p=0.25)$

And for this case we want to find the following probability:

$P(X=0)$

And we can use the probability mass function given by:

$P(X) = nCx (p)^x *1-p)^{n-x}$

And replacing we got:

$P(X=0)= (2C0) (0.25)^0 (1-0.25)^{2-0}= 0.5625= \frac{9}{16}$