Question

In a lottery, 5 numbers are drawn (without replacement) out of 90 (the numbers are 1 through 90).Find the probability that the number 7 is one of the numbers drawn.

Answer 1

The probability that the number 7 is one of the numbers drawn is 1/18 or 0.0556.

Explanation:

We have on number (7) in 90 possible numbers. There are 5 draws, without replacent.

The number 7 can be drawn in the first, second, third, fourth or fifth draw.

The probability of being picked in the first draw is:

`P=(1)/(90)`

The probability of being picked in the second draw is:

`P=(89)/(90)*(1)/(89)=(1)/(90)`

Note: in this case, is the probability of not being picked in the first draw and picked in the second, with one number less (already picked).

The probability of being picked in the third draw is:

`P=(89)/(90)(88)/(89) (1)/(88)=(1)/(90)`

The probability is the same for each draw. This can also have been realized by the fact that if the 7 is picked, in any draw, the replacement doesn't matter anymore.

The chances are the sum of the previous ones:

`P=(1)/(90)+ (1)/(90)+ (1)/(90)+ (1)/(90)+ (1)/(90)=(5)/(90) =(1)/(18) =0.0556`