Finding n and p in binomial distribution.

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Presentation transcript:

Finding n and p in binomial distribution.

Example 1 Evan likes to play two games of chance, A and B. For game A, the probability that Evan wins is 0.9. He plays game A seven times. Find the probability that he wins exactly four games. For game B, the probability that Evan wins is p . He plays game B seven times. (b) Write down an expression, in terms of p, for the probability that he wins exactly four games. (c) Hence, find the values of p such that the probability that he wins exactly four games is 0.15.

Example 2 Jack shoots arrows at a target, with probability of 0.3 of hitting the target. All shots are independent of each other. Calculate the minimum number of shots required for the probability of at least one shot hitting the target to exceed 0.99. Using the binomial probability formula:

A lot of work to obtain the answer this way. Using inverse normal on your CAS calculator for Example 2 above. In the Calculator screen Menu Probability Distributions Inverse Binomial N Probability of zero shots is 1-0.99=0.01 The minimum number of shots is 13

Exercise 14 C

Example 3 Jack shoots 10 arrows at a target, with probability of 0.3 of hitting the target. All shots are independent of each other. Find the range of successful outcomes for the cumulative probability of 0.9556. When matrix display is selected: