Formulae used/concept:
p + q = 1
P(x=r) = P(X = r) =nCr p^r(1-p)^(n-r)
When number of successes are more and more sample space are present.
where,
p = probability of success
q = probability of not success
n = number of sample space done
r = outcome
Ques 1: A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
1. 5 successes?
2. At least 5 successes?
3. At most 5 successes?
Solve: total number on die until are 0,1,2,3,4,5,6
Therefore,
S = 0,1,2,3,4,5,6
Odd number = 1,3,5
n(odd) = 3
P(odd) = 3/6 = ½
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Ques 2: A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two success.
Solve: Download in pdf format
Ques 3: There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
Solve: Download in pdf format
Ques 4: Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that?
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?
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Ques 5: The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs
1. none
2. not more than one
3. more than one
4. at least one
will fuse after 150 days of use.
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Ques 6: A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
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Ques 7: In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
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Ques 8: Suppose X has a binomial distribution B (6,1/2). Show that X=3 is the most likely outcome.
{Hint: P(x=3) is the maximum among all P(xi), xi=0,1,2,3,4,5,6}
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Ques 9: On a multiple-choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answer just by guessing?
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Ques 10: A person buys a lottery ticket in 50 lotteries, in which his chance of winning a prize is 1/100. What is the probability that he will win a prize?
a) at least once
b) exactly once
c) at least twice?
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Ques 11: Find the probability of getting 5 exactly twice in 7 throws of a die.
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Ques 12: Find the probability of throwing at most 2 sixes in 6 throws of a single die.
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Ques 13: It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
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