Question

Question 1: Estimate the probabilities (as decimals) of the following events occurring, under the assumptions of randomness and independence (make sure to describe your process):

Hitting a randomly placed battleship (4 squares in length, and 1 square in width) on a 10 by 10 grid by selecting a single square.

Answer 1

P(hitting a randomly placed battleship) = 4/100 = 0.04 [ANSWER]

Explanation:

The total no. of squares on a 10 by 10 grid = 10*10 = 100

The no. of squares containing the battleship = 4*1 = 4    [Since, the battleship is 4 squares in length and 1 square in width]

Thus, the probability of hitting a randomly placed battleship = (No. of squares containing the battleship)/(Total no. of squares)

[Using Probability = (No. of favorable outcomes)/(Total no. of outcomes)]

Therefore, probability of hitting a randomly placed battleship = 4/100 = 0.04

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.