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Dafna1 [17]
3 years ago
15

Mr. Scott had $90 to spend at the hockey game. He spent 31/45 on his ticket. Then he spent 3/7 of his remaining money at the con

cession stand. On his way back to his seat, he saw a hat for $18 he wanted. Does he have enough to buy the hat? Show your thinking.
Mathematics
1 answer:
postnew [5]3 years ago
7 0
31/45 of 90 leaves him with 62. 3/7 of 62 makes 26.5 so yes he have money left to buy the hat
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Answer:

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Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of guests until the next one pays by American Express credit card

The probability that a guest paying by American Express credit card is, <em>p</em> = 0.20.

The random variable <em>X</em> follows a Geometric distribution since it is defined as the number of trials before the first success.

The probability mass function of <em>X</em> is:

P(X=x)=(1-p)^{x}p;\ x=0,1,2,3...,\ 0

(a)

The expected value of a Geometric distribution is:

E(X)=\frac{1-p}{p}

Compute the expected number of guests until the next one pays by American Express credit card as follows:

E(X)=\frac{1-p}{p}

         =\frac{1-0.20}{0.20}

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Thus, the expected number of guests until the next one pays by American Express credit card is 4.

(b)

Compute the probability that the first guest to use an American Express is within the first 10 to checkout as follows:

P(X=10)=(1-0.20)^{10}\times0.20

                 =0.1073741824\times 0.20\\=0.02147483648\\\approx0.0215

Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

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Answer:

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