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Introductory Probability- Compound and Independent Events, Mutually Exclusive Events, Multi-Stage Experiments
Q: If (1-3p)/2, (1+4p)/3, (1+p)/6 are the probabilities of three mutually exclusive and exhaustive events, then find the value(s) of p.
Q: What is the probability of a leap year having 53 Saturdays or 53 Sundays?
Q: A box contains 10 good articles and 6 defective articles. One item is drawn at random. What is the probability that it is either good or has a defect?
Q: The probabilities that a student will obtain grades A,B,C or D are 0.30,0.35,0.20 and 0.15 respectively. What is the probability that the student will receive atleast grade C?
Q: If the probability of A failing in an exam is 0.2 and of B failing is 0.3, then what is the probability of either A failing, or B failing?
Q: A bag contains 7 red and 2 white balls and another bag contains 5 red and 4 white balls. Two balls are drawn, one from each bag. What is the probability that both balls are white?
Q: Two athletes A and B participate in a race along with other athletes. If the chance of A winning the race is 1/16 and that of B winning the same race is 1/8, what is the chance that neither wins the race?
Q: Three integers are chosen at random from first twenty integers. The probability that their product is even is?(NOTE: For this question, basic Permutation and Combination knowledge is required)
Q: An integer is chosen randomly from the numbers 1,2,…,25. What is the probability that the chosen number is divisible by 3 or 4?
Q: The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probabilities 0.2, then P(not A)+P(not B) = ?
Q: A bag contains x white and y black balls. Two players A and B alternately draw a ball from the bag and then replace it every time after the draw. A begins the game. If the probability of A winning (A player wins when he draws a white ball) is twice the probability of B winning, then find x:y.
Q: A fair coin is tossed n times. Let X=number of times head occurs. If P(X=4), P(X=5) and P(X=6) are in AP, find the value(s) of n.
Q: A person writes four letters and addresses four envelopes. If the letters are placed in the envelopes at random, then what is the probability that all the letters are not placed in the correct envelopes?
Q: A card is drawn from a pack of 52 cards. Let the events be defined as follows:
A : card drawn is red.
B : card drawn is an ace.
C : card drawn is a spade.
Find P(A/B), P(B/C),P(C/A),P(A/C).
Q: Two balls are drawn without replacement one after the other from a bag having 5 white and 8 black balls. What are the chances that the second ball drawn is black?
Q: Let probability that a person has cancer be 0.01. There are two tests T1 and T2. Probability of a test coming positive given that person had cancer is 0.9. Probability of a test being negative given that person did not have cancer is 0.8. What is the probability that a person has cancer given that both T1 and T2 came out positive?
Q: In a game, 3 coins are tossed. A person is paid 5 rupees if he gets all heads or all tails, and he is supposed to pay 3 rupees if gets one head or two heads. What can he expect to win on an average per game?
Q: A number x is selected from first 100 natural numbers. Find the probability that x satisfy the condition x + 100/x > 50
Q: There are three events A, B and C one of which must, and only one can happen, the odd are 8 to 3 against and 2 to 5 for B. Find the odd, against C.
Complete Tutorial with Problems and Solutions :
Companion MCQ Quiz #1 for Probability- test how much you know about the topic. Your score will be e-mailed to you at the address you provide.
Read the Questions in the document below and fill up your answers in the Answer Submission form.
In case you're interested, here are the tutorial we have, related to probability and probabilistic distributions :