Lecture 13 Bernoulli’s Formula. The Most Probable Number of Occurrences of an Event If n

less than two times.

no less than two times.

Solution.

1. 
   
   
2. 
   
   

Example 6. We toss a coin eight times. Find the probability that the Heads comes up no more than three times.

Solution. We have



.

Example 7. There are 10 white and 40 red balls in the box. We successively draw 14 balls, register the colour of each drawn ball and replace it into the box. Determine the most probable number of occurrences of a white ball.

Solution. Here .

Using the double inequality



at the values of n, p and q indicated, we obtain

,

i.e. .

Thus, the problem admits of two solutions:



Example 8. The probability of a marksman hitting the target is 0.8. He fires 20 shots. Determine the most probable number of times he hits the target.