The current Powerball jackpot is estimated to be $193 million. The Powerball lottery is decided every Wednesday and Saturday nig
ht by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. What would the minimum jackpot need to be in order to make purchasing a ticket not detrimental for the player? Round to the nearest dollar.
1 answer:
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Answer:
10
Step-by-step explanation:
If there’s a direct correlation between variables x and y, it can be expressed as
y = kx,
where y is the dependent variable
x is the independent variable
k signifies the constant of variation
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For the first scenario
y = 400
x = r
using y = kx, we can derive the relation:
400 = kr
To find k here:
k = 400/r
For the second scenario
y = r
x = 4
again using y = kx, the relationship is given by:
r = 4k
Solving for k:
k = r/4
Since both conditions provide the same equation, k will have the same value in both cases.
Thus, we conclude:
400/r = r/4
=> 400*4 = r*r
=> 1600 = r^2
Hence, r is calculated to be 40.
Thus, k = r/4 = 40/4 = 10.
The constant of variation is confirmed to be 10, which is the correct answer.
Verification:
k = 400/r = 400/40 = 10
Answer:
a) 2.60x10^-7
b) 5.31x10^-5
c) 2.19x10^-3
Step-by-step explanation:
X=the number of hits
Probability can be determined by taking the number of successful outcomes and dividing it by the total number of possible outcomes.
Now
a) P(X=6)=P({1, 1, 1, 1, 1, 1})=6/40*5/39*4/38*3/37*2/36*1/35=2.60x10^-7
b) P(X=5)=P({0, 1, 1, 1, 1, 1})+P({1, 0, 1, 1, 1, 1})+...+P({1, 1, 1, 1, 1, 0}), and each scenario carries the same probability
P(X=5)=6P({1, 1, 1, 1, 1, 0})=6*(6/40*5/39*4/38*3/37*2/36*34/35)=5.31x10^-5
c) P(X=4)=P({0, 0, 1, 1, 1, 1})+...+P({1, 1, 1, 1, 0, 0}), where each case has an identical probability.