1. P(A U B) 0.7 and P(A u B\') 0.7, what is PA)? zo 0.7 0.7 PAJ+ .2 2. Based on

Question

1. P(A U B) 0.7 and P(A u B') 0.7, what is PA)? zo 0.7 0.7 PAJ+ .2 2. Based on past history, the owner of a sporting goods store has determined the following: i. The probability that a randomly selected customer will buy socks is.15 ii. The probability that a customer will buy sneakers is2 iii The probability that a customer will buy socks but not sneakers is. What is the probability that a randomly selected customer will buy neither socks nor shoes? P(A): 0-15. 0 3 0.06 0.11 3. A total of two hundred students took MATH 300 last semester of which 17 failed the course. Out of the two hundred students, 140 were in Professor Ant's class, and among the students in Professor Ant's class, 14 of them failed. Determine the probability that a student randomly selected from the total group of 200 students failed given that the student was NOT in Professor Ant's class : Ants class. _ : failed,n Ant's clas

Explanation / Answer

Answer to question # 1)

P(A u B) = 0.7

P(A u B') = 0.7

.

P(A u B) = P(A) + P(B) - P(A n B) ............. eq(1)

.

P(A u B') = P(A) + P(B') - P(A n B')

P(A n B') = P(A) - P(A n B)

Thus P(A u B') = P(A) + P(B') - [P(A) - P(A n B)]

P(B') = 1 - P(B)

thus P(A u B') = P(A) + 1 - P(B) - P(A) + P(A n B)

P(A u B') = 1 - P(B) + P(A n B) ....... eqn (2)

.

Now we rewrite the two equations:

P(A u B) = P(A) + P(B) - P(A nB)

P(A u B') = 1 - P(B) + P(A n B)

On adding these two equations we get

P(A u B) + P(A u B') = 1 + P(A)

We got P(A u B) = 0.7 and P(A u B') = 0.7

On plugging these vlaues in the above equation we get

0.7 + 0.7 = 1 + P(A)

1.4 - 1 = P(A)

0.4 = P(A)

hence the answer to question# 1 is 0.4

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