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You are about to get on a plane to Seattle, you want to know whether you have to bring an umbrella or not. You call three of your random friends and as each one of them if it's raining. The probability that your friend is telling the truth is 2/3 and the probability that they are playing a prank on you by lying is 1/3. If all 3 of them tell that it is raining, then what is the probability that it is actually raining in Seattle.

31You have been given the data on Facebook user's friending or defriending each other. How will you determine whether a given pair of Facebook users are friends or not?

35You are given 50 cards with five different colors- 10 Green cards, 10 Red Cards, 10 Orange Cards, 10 Blue cards, and 10 Yellow cards. The cards of each colors are numbered from one to ten. Two cards are picked at random. Find out the probability that the cards picked are not of same number and same color.

36Pick up a coin C1 given C1+C2 with probability of trials p (h1) =.7, p (h2) =.6 and doing 10 trials. And what is the probability that the given coin you picked is C1 given you have 7 heads and 3 tails?

59A building has 100 floors. Given 2 identical eggs, how can you use them to find the threshold floor? The egg will break from any particular floor above floor N, including floor N itself.

69You have 2 dices. What is the probability of getting at least one 4? Also find out the probability of getting at least one 4 if you have n dices.

108How will you test that there is increased probability of a user to stay active after 6 months given that a user has more friends now?

65What is the probability of pulling a different shape or a different colour card from a deck of 52 cards?

40You can roll a dice three times. You will be given $X where X is the highest roll you get. You can choose to stop rolling at any time (example, if you roll a 6 on the first roll, you can stop). What is your expected pay-out?

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