Respuesta :
Answer:
(a) 9.9321*10^{-11}
(b) 6.0498*10^{-11}
(c) 7.7120^{-11}
(d) 1.6417 times more probable
Step-by-step explanation:
(a) The probability of winning a 6/49 lottery is given by:
[tex]P = \frac{1}{49*48*47*46*45*44} =9.9321*10^{-11}[/tex]
(b) The probability of winning a 6/53 lottery is given by:
[tex]P = \frac{1}{53*52*51*50*49*48} =6.0498*10^{-11}[/tex]
(c) The probability of winning a 6/51 lottery is given by:
[tex]P = \frac{1}{51*50*49*48*47*46} =7.7120^{-11}[/tex]
(d) The ratio between the probabilities of winning the 6/49 lottery and winning the 6/53 lottery is:
[tex]r=\frac{9.9321*10^{-11}}{6.0498^{-11}}\\r=1.6417[/tex]
It is 1.6417 times more probable.
The probability of winning a 6/49, 6/53, and 6/51 lottery is 9.9321 × 10⁻¹¹, 6.0498 × 10⁻¹¹, and 7.7120 × 10⁻¹¹. The ratio between the probabilities of winning the 6/49 lottery and winning the 6/53 lottery is 1.6417.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
In 1990, California switched from a 6/49 lottery to a 6/53 lottery.
Later, the state switched again to a 6/51 lottery.
a) The probability of winning a 6/49 lottery is given by
[tex]P(6/49) = \dfrac{1}{49*48*47*46*45*44} = 9.9321* 10^{-11}[/tex]
b) The probability of winning a 6/53 lottery is given by
[tex]P(6/53 ) = \dfrac{1}{53*52*51*50*49*48} = 6.0498* 10^{-11}[/tex]
c) The probability of winning a 6/51 lottery is given by
[tex]P(6/51) = \dfrac{1}{51*50*49*48*47*46} = 7.7120* 10^{-11}[/tex]
d) The ratio between the probabilities of winning the 6/49 lottery and winning the 6/53 lottery will be
[tex]r = \dfrac{ 9.9321* 10^{-11}}{ 6.0498* 10^{-11}}\\\\r = 1.6417[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
