Question

The probability of winning in a lottery is 1/100. You buy a ticket for 50 different lotteries. ◦ What is the probability that you win exactly in one of these 50 lotteries? ◦ What is the probability that you win at least one of these 50 lotteries?

Answer 1

p =0.01

n=50

The probability of getting exactly x= 1 is given by

${n \choose x}$ *p^x*(1-p)^n-x

${50 \choose 1}$ *0.01¹ *(0.99)⁴⁹

^{= 0.30556}

^{the probability that at least one is given by 1-P(x=0);}

^{the probability x=0 is:}

${50 \choose 0}$ *0.01⁰*0.99⁵⁰

=0.6050;

1-0.06050

=0.395