Let 𝜉 ! , 𝜉 " , ... be a sequence of independent trials with two possible outcomes, "0" and "1" where "1" represents the success of Type-I, and "0" denotes the success of Type-II. For nonnegative integers 𝑘 # and 𝑘 $ using a reward scheme, we obtained the distribution of the number of trials (𝑊) until the sum of consecutive rewards of Type-I is equal to or exceeds the level 𝑘 # , or the sum of consecutive rewards of Type-II is equal to or exceeds the level 𝑘 $ . The geometric distributed

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... are studied by Eryılmaz et al. in [1]. In this study, the survival function of 𝑊 is obtained for binary sequence with Bernoulli and exponential rewards as well as geometric rewards. A simulation study is performed to compare the theoretical and simulated probabilities. Proportion estimates are also discussed for distribution of 𝑊 with geometric rewards.