(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score? Explain your reasoning.

The probability of successful  long hit is greater than 0.7083

Step-by-step explanation:

Solution

The expected value for long hit is given below

P (successful hit) * 4.2 + P (Unsuccessful hit) *5.4

so,

= P * 4.2 + (1-p) * 5.4

= 5.4 - 1.2p

Now,

If the expected value of long hit is less than  that of the short it

Then,

5.4 - 1.2p <4.55

P> (5.4 - 4.55)/1.2

P> 0.7083

Therefore the probability of successful  long hit is greater than 0.7083

Note:

Due to my research and findings to this example, the complete question for  is attached below, i solved or Question 2(d) only