I really don’t understand this section. Someone help, please? ting 4.171 Three b
ID: 2949251 • Letter: I
Question
I really don’t understand this section. Someone help, please? ting 4.171 Three balanced coins are tossed simultaneously the Find the probability of obtaining three heads, given that at least one of the coins shows heads a. Solve using an equally likely sample space. b. Solve using the formula for conditional probability. same m. Find P(A C). n. Are events A and B mutually exclusive? Explain. o. Are events B and C mutually exclusive? Explain. p. Are events A and Cmutually exclusive? Explain. q. Are events A and B independent? Explain. r. Are events B and C independent? Explain. s. Are events A and C independent? Explain. If the wn in ue. ency n for 4.12 Events A and B are mutually exclusive and P(A) 0.4 and P(B) 0.3. a. Find P(A and B). b. Find P(A or B). c. Find P(A B). d. Are events A and B independent? Explain. ually y will abil- Iways also m of 4.13 Events E and F have probabilities P(E) 0.5, P(F) 0.4, and P(E and F) = 0.2. a. Find P(E or F). b. Find P(E|F). c. Are E and F mutually exclusive? Explain. d. Are E and F independent? Explain. e. Are G and H independent? Explain. 4.14 Janice wants to become a police officer.She must pass a physical exam and then a written exam. Records show that the probability of passing the physical exam is 0.85 and that once the physical is passed, the proba- bility of passing the written exam is 0.60. What is the probability that Janice passes both exams? are and"Explanation / Answer
4.12)
P(A or B) = P(A) + P(B) - P(A and B) {always true}
now when A and B are mutually exclusive
then P(A and B) = 0
here A and B are mutually exclusive
a) hence P(A and B) = 0
b) P(A or B) = P(A)+ P(B) - P(A and B)
= 0.4 + 0.3 -0
=0.7
c)
P(A |B) = P(A and B)/P(B) = 0 { as P(A and B ) = 0}
d) No ,
A and B are not independent
P(A and B) = 0
P(A and B) does not equal P(A) * P(B)
note that P(A and B) = P(A)*P(B) when A and B are independent
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