Two goals post are 8m apart. A footballer is 34m from one and 38m from the other. Within what angle must he kick the ball if he
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Answer: Our required probability is 0.83.
Step-by-step explanation:
Since we have given that
Number of dices = 2
Number of fair dice = 1
Probability of getting a fair dice P(E₁) =
Number of unfair dice = 1
Probability of getting a unfair dice P(E₂) =
Probability of getting a 3 for the fair dice P(A|E₁)=
Probability of getting a 3 for the unfair dice P(A|E₂) =
So, we need to find the probability that the die he rolled is fair given that the outcome is 3.
So, we will use "Bayes theorem":
Hence, our required probability is 0.83.
Let's try to find some primes that divide this number.
The number is not divisible by 2, because it is odd.
The number is divisible by 3 though, because the sum of its digits is:
So, we can divide the number by 3 and keep going with the factorization:
This number is again divisible by 3, because
We have
This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have
And 557 is prime, so we're done. This means that the prime factorization of 65169 is