Searches related to Probability questions - A person frequents one of the two restaurants KARIM or NAZEER, choosing Chicken's item 70% of the time and fish's item 30% of the time. Regardless of where he goes , he orders Afghani Chicken 60% of his visits. (a) The next time he goes into a restaurants, what is the probability that he goes to KARIM and orders Afghani Chicken. (b) Are the two events in part a independent? Explain. (c) If he goes into a restaurants and orders Afghani Chicken, what is the probability that he is at NAZEER. (d) What is the probability that he goes to KARIM or orders Afghani Chicken or both?

a) 0.42

b) Independent

c) 30%

d) 0.88

Explanation:

Person chooses Chicken's item : 70% = 0.7

Person chooses fish's item : 30% = 0.3

Visits in which he orders Afghani Chicken = 60% = 0.6

a) Probability that he goes to KARIM and orders Afghani Chicken:

P = 0.7 * 0.6 = 0.42

b) Two events are said to be independent when occurrence of one event does not affect the probability of the other event's occurrence. Here the person orders Afghani Chicken regardless of where he visits so the events are independent.

c)  P = 0.30 because he orders Afghani Chicken regardless of where he visits.

d)  Let A be the probability that he goes to KARIM:

P(A) = 0.7 * ( 1 - 0.6 ) = 0.28

Let A be the probability that he orders Afghani Chicken:

P(B) =  0.3 * 0.6 = 0.18

Let C be the probability that he goes to KARIM and orders Afghani chicken:

= 0.7 * 0.6 = 0.42

So probability that he goes to KARIM or orders Afghani Chicken or both:

P(A) + P(B) + P(C) = 0.28 + 0.18 + 0.42 = 0.88

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