The probability of waiting 2 minutes or longer for checkout at a particular supermarket counter is 0.3. On a given day, a man and his wife decide to shop individually at the market, each checking out at different counters. They both reach the counters at the same time. What is the probability that one or the other or both will wait 2 minutes or longer?

The probability answer is 69/100

Step-by-step explanation:

The probability of waiting 2 minutes or longer = 0.3= (3/10)

The probability of not waiting longer = 1 - (3/10) = (7/10)

For the man,

P(waiting 2 mins or longer) = 3/10

For the woman,

P(waiting 2 mins or longer) = 3/10

Therefore,

The probability that one or the other or both will wait 2 minutes or longer

= P(man waits 2 mins or longer) or P(woman waits 2 mins or longer) or P(both waits 2 mins or longer)

= (3/10) or (3/10) or ( (3/10) and (3/10) )

= (3/10) + (3/10) + ( (3/10) X (3/10) )

= (6/10) + (9/100)

= (69/100)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.