Question 1 - Important Probability Questions - Chapter 14 Class 10 Probability

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Question 1 Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days?Shyam and Ekta can visit the shop on Tuesday, Wednesday, Thursday, Friday & Saturday. Let T = Tuesday, W = Wednesday, Th = Thursday, F = Friday and S = Saturday. Then, total possible outcomes are (T, T) (T, W) (T, Th) (T, F) (T, S) (W, T) (W, W) (W, Th) (W, F) (W, S) (Th, T) (Th, W) (Th, Th) (Th, F) (Th, S) (F, T) (F, W) (F, Th) (F, F) (F, S) (S, T) (S, W) (S, Th) (S, F) (S, S) Total number of outcomes = 25 If Shyam and Ekta visit the shop on same day, Favourable outcomes = (T, T), (W, W), (Th, Th), (F, F), (S, S) = 5 outcomes Probability = ( )/( ) = 5/25 = / (ii) If Shyam and Ekta visit the shop on consecutive days, Favourable outcomes = (T, W), (W, T), (W, Th), (Th, W), (Th, F), (F, Th), (F, S), (S, F) = 8 outcomes Probability = ( )/( ) = / (iii) If Shyam and Ekta visit the shop on different days, Now, P (Shyam and Ekta visit on same days) + P (Shyam and Ekta visit on different days) = 1 5/25 + P(Shyam and Ekta visit on different days) = 1 P(Shyam and Ekta visit on different days) = 1 1/5 = (5 1)/5 = /