A submarine attempts to sink an aircraft carrier It will be

A submarine attempts to sink an aircraft carrier. It will be successful only if two or more torpedoes hit the carrier. If the probability of a hit is 40% for each torpedo, w probability that the carrier will be sunk if the: Submarine fires two torpedoes? Submarine fires three torpedoes? Submarine fires four torpedoes? A precision guided munition has a Circular Error Probability at 66.67% of 10m. This means that 2/3^rds of all hits are within 10m of the target. A series of six test drops have been made. Find the probability that \"one of the weapons hit within 10m of the target. Find the Probability that at least one weapon hit within 10m of the target. e weapons test is successful if the probability is 90% that three or more weapons will \'t within 10m of the target. Is the test successful? Immortal Monkey: An immortal monkey is sitting at a keyboard typing keys at random, e monkey will ultimately type Shakespeare\'s 14Sth sonnet. Find the probability of the monkey typing the sonnet. Estimate the time needed for this. Compare the time to do this to the estimated age of the universe, 10^10 years. Use the following assumptions: the monkey can type two characters per second, the sonnet is reproduced exactly as listed below, there are 34 possible characters (a through *), space, period, comma, quote, colon, semicolon, apostrophe, and carriage return (each line ends with one), and the probability of pressing any key is uniformly distributed. those lips that love\'s own hand did make breathed forth the sound that said \"I hate\" to me that languished for her sake; but when she saw my woeful state, straight in her heart did mercy come, chiding that tongue that, ever sweet, was used in giving gentle doom, and taught it thus anew to greet: \"I hate\" she altered with an end that followed it as gentle day doth follow night, who like a fiend from heav\'n to hell is flown away. \"I hate\" from hate away she threw, and saved my life, saying \"not you.\"

Solution

6)

We use the binomial theorm pdf function to solve the problem:

If 2 or more torpedoes hit the carrier.
P(hits) = .40

Hence,

a.P(fires 2 torpedoes) = 2C2*(.4^2)*(.6^0) = .16
b.P(fires 3 torpedoes) = 3C2(.4^2)(.6^1) +3C3(.4^3)(.6^0) = .288+.064 = .352
c.P(fires 4 torpedoes) = 4C2(.4^2)(.6^2)+4C3(.4^3)(.6^1)+4C4(.4^4)(.6^0) = .5248