Using the Poisson formula, find the following probabilities. (show all work and round the final answer to 3 decimal places) a)P(x=4) for λ=5.2 b)P(x≤1) for λ=5.2

Please do the following question with program R.

assume the n trails is independent and that p is the probability of success on a given trail. Use the binomial probability formula to find P(x) n=5, x=3, p=0.3

Sarah and Thomas are going bowling. The probability that Sarah scores more than  175  is  0.5 , and the probability that Thomas scores more than  175  is  0.1 . Their scores are independent. Round your answers to four decimal places, if necessary.   (a) Find the probability that both score more than  175 .   (b) Given that Thomas scores more than  175 , the probability that Sarah scores higher than Thomas is  0.4 . Find the probability that Thomas scores more than  175  and Sarah scores higher than Thomas.

If you have λ = 4.2, what is the probability that P(x < 2)?

B. Find the following probabilities using the t-table if X~t20 a. P(T > 0.860) b. P(T < - 1.325) C. Find k such that P(k< T< 2.947) = 0.845 when T~t15