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PS Questions from Modern Math/Stats

Three snipers shoot a certain target. Their probabilities of hitting the target are 0.9, 0.7, and 0.5 respectively. The snipers make one salvo. What is the probability that exactly one sniper hit?
Probability that an event A doesn't occur = 1-P(A) where P(A) is the probabiity that A occurs. The probability that the target is hit by the FIRST shoo...
Tue, 12 Oct, 2021 at 3:54 PM
One coin in a collection of 65 has two heads. The rest are fair. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row, what is the probability that it is the two-headed coin?
The Probability of selecting a fair coin= 64/65 The Probability of getting 6 heads in a row with the fair coin= (1/2)^6= 1/64 The Probability of selecting...
Tue, 12 Oct, 2021 at 3:55 PM
A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) What is the probability of getting an even number in on
The probability of the faces are proportional to the numbers on them, =>Let the probabilities of faces bearing 1,2,6 be x,2x,......,6x respectively. Sin...
Tue, 12 Oct, 2021 at 3:55 PM
Two cards are drawn successively from a deck of 52 cards. What is the probability that the second card is higher in rank than the first card?
The probability that the second card has the same face value as the first (Implying they both have the same face value) is 3/51, (As irrespective of what va...
Tue, 12 Oct, 2021 at 3:55 PM
ABCDEFGH is an octagon. Two vertices of the octagon are selected at random. Find the probability that these vertices form a diagonal of the octagon.
The question is of selection as order is NOT important here. Selecting vertices A and B is same as B and A. Number of ways to select two vertices is 8C2 =2...
Tue, 12 Oct, 2021 at 3:56 PM
Of the 150 people at a party, 70 were women, and 30 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
Number of Men are = 150-70=80 men Number of women who did NOT try the appetizer = 70-30 = 40 women out of 50 people who did NOT try the appetizer. Hence n...
Tue, 12 Oct, 2021 at 3:56 PM
During the 28-day month of February, an appliance store sold a different number of refrigerators each day. If the store recorded at least one sale each day, and set a store record with 70 sales on February 8, what is the minimum number of r
Sale on 8th Feb = 70. With a minimum of 1 sold and different number of refrigerators sold each day, we have the count of refrigerators sold in the 27 days a...
Tue, 12 Oct, 2021 at 3:56 PM
Jane sold cookies at a fair for 96 cents each; she then used that money to buy popsicles for 30 cents each. If she had no money left over, what is the fewest number of cookies she could have sold?
Let Jane sell "a" cookies 96 cents/cookie. Thus total money earned from cookies = a*96 cents Let Jane buy "b" popsicles 30 cents/popsic...
Tue, 12 Oct, 2021 at 3:56 PM
According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skating. If the number of people who enjoy neither skiing nor skating is 2 times the number of people who enjoy both skiing and skating, how many people surveyed enjoy neithe
SOLUTION: Its a question that tests on basics of set theory and overlapping sets in particular. Let "x" be the number of people enjoying BOTH sk...
Tue, 12 Oct, 2021 at 3:56 PM
In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent of the seniors who are taking calculus are also taking physics. If 10 percent of the seniors are taking neither calculus nor physics, what percent of th
SOLUTION : A NEW OG 2021 QUESTION Its a question testing on your application skills in Overlapping sets(Concept-Set Theory). Seniors taking Calculus (C)= ...
Tue, 12 Oct, 2021 at 3:56 PM
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