Respuesta :
Answer:
The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the first five numbers are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
First five numbers:
Desired:
5 correct numbers, from a set of 5. So
[tex]D = C_{5,5} = \frac{5!}{5!(5-5)!} = 1[/tex]
Total:
5 numbers from a set of 69. So
[tex]T = C_{69,5} = \frac{69!}{5!(69-5)!} = 11238513[/tex]
Probability:
[tex]P_{5} = \frac{D}{T} = \frac{1}{11238513}[/tex]
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Sixth number:
1 from a set of 26
Then
[tex]P_{6} = \frac{1}{26}[/tex]
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Probability of winning the prize
[tex]P = P_{5} \times P_{6} = \frac{1}{11238513} \times \frac{1}{26} = \frac{1}{292201338}[/tex]
The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]
