Anthony Papantonis, owner of Nauset Construction, is bidding on two projects, A and B. The probability that he wins project A is 0.50 and the probability that he wins project B is 0.80. Winning Project A and winning Project B are independent events.

a. What is the probability that he wins project A or project B?
b. What is the probability that he does not win either project?

a) the probability of winning A and B is 0.4 (40%)

b) the probability of not winning either project is 0.1 (10%)

Step-by-step explanation:

if 2 events are independent then

P(A∩B)=P(A)*P(B)

where

P(A)= probability of winning project A

P(B)= probability of winning project B

P(A∩B)= probability of winning projects A and B

replacing values

P(A∩B)=P(A)*P(B) = 0.50 * 0.8 = 0.4

b) since

P(A∪B) = P(A) + P(B) - P(A∩B) = 0.50 + 0.8 - 0.4 = 0.9

where

P(A∪B) =  probability of winning A or B

therefore

probability of not winning either project = 1 - P(A∪B) = 1 - 0.9 = 0.1 (10%)

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: