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Probability of at least one success (or none) in n binomial trials

This type of question, asked 8 times: 2 May 2023 S1, 3 May 2023 S1, 3 May 2023 S2, 15 Apr 2026 S2, 16 Apr 2026 S1, 18 Apr 2026 S2, 19 Apr 2026 S2, 14 May 2026 S1. All 8 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    139
    Ten bulbs are drawn successively, with replacement, from a lot containing 10% defective bulbs, then the probability that there is at least one defective bulb, is

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  2. Question 2

    3 May 2023 S1

    144
    Two cards are drawn successively with replacement from a pack of 52 cards. Let X denote the number of jacks obtained. Then P(X=1)+P(X=2)P(X=1)+P(X=2) equals

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  3. Question 3

    3 May 2023 S2

    115
    Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Let x denote the random variable of number of kings obtained in the two drawn cards. Then P(x=1)+P(x=2)P(x=1)+P(x=2) equals

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  4. Question 4

    15 Apr 2026 S2

    100
    The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......

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  5. Question 5

    16 Apr 2026 S1

    100
    Two dice are thrown successively 4 times and getting a doublet is called a success. The probability of getting at least 1 success is

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  6. Question 6

    18 Apr 2026 S2

    98
    A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is …\ldots

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  7. Question 7

    19 Apr 2026 S2

    97
    The probability that a bomb will hit the target is 0.80.8. Out of 66 bombs dropped, probability that at least 11 will miss the target is...

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  8. Question 8

    14 May 2026 S1

    98
    The probability that a person hits a target is 0.60.6. If he fires 55 shots at the target, then the probability that he hits the target at least once is

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