Binomial: a relation between two probabilities fixes n or p, then find another probability
This type of question, asked 7 times: 2021 Paper 1, 2021 Paper 10, 2021 Paper 25, 14 Jun 2022, 26 Jun 2022, 27 Jun 2022, 10 Apr 2023. All 7 questions below, oldest first.
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Question 1
2021 Paper 1
77An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :Tap an option to check your answer.
Question 2
2021 Paper 10
74Let 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:Tap an option to check your answer.
Question 3
2021 Paper 25
77A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is:Tap an option to check your answer.
Question 4
14 Jun 2022
77If a random variable follows the Binomial distribution such that , then the value of is equal toTap an option to check your answer.
Question 5
26 Jun 2022
77Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is:Tap an option to check your answer.
Question 6
27 Jun 2022
77Let be a random variable having binomial distribution . If , then the sum of the mean and the variance of is:Tap an option to check your answer.
Question 7
10 Apr 2023
158Let a die be rolled times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is , then is equal to:Tap an option to check your answer.