June 2021

The probability that both stages of a two-stage missile will function correctly is 0.95. The probability that the first stage will function correctly is 0.98. What is the probability that the second stage will function correctly given that the first one does?

There are three candidates for president of Silk Residences Condominium Unit Owners Association. The probability that Albert will be elected is 0.3, the probability that Bryan will be elected is 0.5 and the probability that Charlie will be elected is 0.2. Should Albert be elected the probability for an increase in monthly dues is 0.8. Should Bryan or Charlie be elected, the probabilities for increase in monthly dues are 0.1 and 0.4, respectively. What is the probability that there is an increase in monthly dues?

Studies have shown that 72.5% of apprehended snatchers in Metro Manila are drug users. In a random sample of 16 apprehended snatchers, what is the probability that exactly 10 of them are drug users?

What is the probability that a waitress will refuse to serve alcoholic beverages to only 2 minors if she randomly selects the I.D.’s of 6 students from among 9 students of which 4 are not of legal age?

A multiple-choice examination has 200 questions, each with 4 possible answers, of which only one is correct. What is the probability that sheer guess work yields from 25 to 30 correct answers for 80 of the 200 problems about which the student has no knowledge?

I was walking along the road at 6kph when a car dashed past me and only missed me by a few inches. From the moment it passed me to its disappearance round a corner I took thirty-one steps and walking on reached that corner with four hundred and thirty-four steps more. Assuming that I walked and the car ran at uniform speeds, what was the speed of the car?

A substance goes into a solution at the rate of 25% of the undissolved portion each minute. If the initial amount was 64/27 grams, what amount (in grams) is undissolved after 6 minutes?

In a certain town there are 1000 married couples. Two-thirds of the husbands who are taller than their wives are also heavier and three-quarters of the husbands who are heavier than their wives are also taller. If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller and heavier than their wives?

M. Poirot and Miss Marple walk into a turned-off escalator to realize that he is able to walk 3 steps during the time she needs to walk only 2. When the escalator is turned-on and it is already working at constant speed, M. Poirot enters again the escalator to realize he needs to take 25 steps to go through it, while Miss Marple realizes she needs only 20 steps to reach its end (at the very same conditions). How many steps are there on the escalator?

A truth serum given to a suspect is known to be 90% reliable when the person is guilty and 99% reliable when the person is innocent. If the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent?