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Relation between P(X = a) and P(X = b) in a binomial: find p, then what is asked

This type of question, asked 12 times: 2 May 2023 S2, 10 May 2023 S1, 11 May 2023 S2, 9 May 2024 S1, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S2, 19 Apr 2025 S1, 20 Apr 2025 S1, 21 Apr 2025 S1, 19 Apr 2026 S1, 20 Apr 2026 S1. All 12 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    103
    Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to

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  2. Question 2

    10 May 2023 S1

    128
    In a Binomial distribution consisting of 5 independent trials, probabilities of exactly 1 and 2 successes are 0.4096 and 0.2048 respectively, then the probability of getting exactly 4 successes is

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  3. Question 3

    11 May 2023 S2

    150
    One hundred identical coins, each with probability p, of showing up heads are tossed once. If 0<p<10<p<1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

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  4. Question 4

    9 May 2024 S1

    124
    In a Binomial distribution with n=4n=4, if 2P(X=3)=3P(X=2)2P(X=3)=3P(X=2), then the variance is

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  5. Question 5

    10 May 2024 S1

    143
    Binomial X, n=6, P(X=4)=135212P(X=4)=\frac{135}{2^{12}}. Variance is

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  6. Question 6

    11 May 2024 S1

    131
    A binomial random variable X satisfies 9P(X=4)=P(X=2)9P(X=4) = P(X=2) when n=6n=6. Then p is equal to

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  7. Question 7

    12 May 2024 S2

    124
    An irregular six faced die is thrown and the probability that, in 5 throws it will give 3 even numbers is twice the probability that it will give 2 even numbers. The number of times, in 6804 sets of 5 throws, you expect to give no even number is

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  8. Question 8

    19 Apr 2025 S1

    119
    If a random variable X follows the Binomial distribution B(33,p)B(33,p) such that 3P(X=0)=P(X=1)3P(X = 0) = P(X = 1), then the variance of X is

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  9. Question 9

    20 Apr 2025 S1

    116
    If X is a binomial variable with range {0,1,2,3,4}\mathbf{\{ 0,1,2,3,4\}} and P(X=3)=3P(X=4)P(X = 3) = 3P(X = 4) then the parameter ' pp ' of the binomial distribution is.

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  10. Question 10

    21 Apr 2025 S1

    101
    If a random variable X follows the Binomial distribution B(10,p)B(10,p) such that 5P(X=0)=P(X=1)5P(X = 0) = P(X = 1), then the value of P(X=5)P(X=6)\frac{P(X = 5)}{P(X = 6)} is equal to

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  11. Question 11

    19 Apr 2026 S1

    98
    If in 66 trials, X is a binomial random variable which follows the relation 9P(x=4)=P(x=2)9P(x = 4) = P(x = 2), then the probability of failure is...

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  12. Question 12

    20 Apr 2026 S1

    98
    A random variable X∼B(n,p)X \sim B(n, p) follows a binomial distribution with n=6n = 6. If 9P(X=4)=P(X=2)9P(X = 4) = P(X = 2), then the probability of success pp is..

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