Question

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) Find the probability of winning first prize in a 6/49 lottery. (b) Find the probability of winning first prize in a 6/53 lottery. (c) Find the probability of winning first prize in a 6/51 lottery. (d) How much more probable is it that one will win the 6/49 lottery than the 6/53 lottery? (Round your answer to the nearest whole number.)

Answer 1

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:

$P = \frac{1}{49*48*47*46*45*44} =9.9321*10^{-11}$

(b) The probability of winning a 6/53 lottery is given by:

$P = \frac{1}{53*52*51*50*49*48} =6.0498*10^{-11}$

(c) The probability of winning a 6/51 lottery is given by:

$P = \frac{1}{51*50*49*48*47*46} =7.7120^{-11}$

(d) The ratio between the probabilities of winning the 6/49 lottery and winning the 6/53 lottery is:

$r=\frac{9.9321*10^{-11}}{6.0498^{-11}}\\r=1.6417$

It is 1.6417 times more probable.