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3 years ago

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The game is played by Drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red power bowl out of a d

rum 26 red balls (numbered 1-29) The jackpot is one by matching all five white balls in any order in the red Powerball.

1 answer:

blsea [12.9K]3 years ago

5 0

Answer:

The expected value for purchasing one ticket for the jackpot = $77.26

Step-by-step explanation:

We first compute the probability mass function for the problem.

Probability of winning the jackpot

One has to get all 5 white ball and the one red ball correctly. There are 69 white balls and 26 red balls.

5 white balls can be selected from 69 with order not important, and 1 red ball selected from 26 red balls in

⁶⁹C₅ × ²⁶C₁ ways = 292,201,338 ways

And there are (5! × 1) different combinations of those winning numbers = 120 combinations (since order isn't important for the 5 numbers of the white balls)

Required Probability of winning

= (120 ÷ 292,201,338) = 0.0000004107

= (4.107 × 10⁻⁷)

To win, one would buy a $2 ticket, and win $193 million.

Amount of winnings = 193,000,000 - 2 = $192,999,998

Probability of losing = 1 - (Probability of winning) = 1 - (4.107 × 10⁻⁷) = 1

To lose, one would buy a $2 ticket and win nothing.

Amount of winnings = 0 - 2 = -$2

So, the probability mass function

X | 192,999,998 | -2

p | (4.107 × 10⁻⁷) | 1

Expected value = E(X) = Σ xᵢpᵢ

E(X) = [(192,999,998) × (4.107 × 10⁻⁷)] + (-2)(1)

E(X) = 79.26 - 2 = $77.26

Hope this Helps!!!

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3 years ago

A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

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$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

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to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

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This implies that,

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This finally simplifies to,

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PART B

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$h(t) = 0$

This implies that,

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We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

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Since time cannot be negative, we discard the negative value and pick,

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