peobability of getting least prime number
Answers
So assuming it's a fair six-sided die with numbers 1,2,3,4,5,6 on it, the prime numbers are 2,3 and 5.
So 3 out of 6 numbers are prime numbers. So in any one roll, the probability of rolling a prime number is 3/6 that is ½.
So probability of not rolling a prime number is also ½.
According to the condition given, in ten rolls, you have to get at least one prime number. So you're allowed to get, 1,2,3,4,5,6,7,8,9 or even 10 prime numbers but not 0 prime numbers. So the only case which will be excluded from the total probability is where you get no prime numbers in your ten individual rolls.
Total probability of all possible events is always 1. Probability of obtaining non prime numbers for each individual roll is ½. Rolling 10 times would mean,
Pr (Non prime numbers for 10 consecutive rolls) = (½)^10
Therefore, Pr (At least one prime number in ten rolls) = 1 - (½)^10 = 1023/1024 (Answer).
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