Question

If two-digit numbers are made with 3, 5, 7 and 9, what is the
probability that the number is
(i) greater than 55
(ii) a prime number
(iii) multiple of 3

Answer 1

Answer:

Hope the answer will help !!

Answer 2

We need to recall the following formula for probability.

• $P(E)=\frac{Number\ of\ favourable\ outcomes}{Total\ outcomes}$

Given:

two-digit numbers are made with $3, 5, 7$ and $9$.

The possible numbers are:

$33,35,37,39,53,55,57,59,73,75,77,79,93,95,97,99$

The total outcomes are $16$.

i) Probability that the number is greater than $55$.

The numbers greater than $55$ are: $57,59,73,75,77,79,93,95,97,99$

The probability that the number is greater than $55$ is,

$P(greater\ than\ 55)=\frac{10}{16}$

$P(greater\ than\ 55)=\frac{5}{8}$

ii) Probability that a number is a prime number

The prime numbers are: $37,53,59,73,79,97$

The probability that a number is a prime number is,

$P(a\ prime\ number)=\frac{6}{16}$

$P(a\ prime\ number)=\frac{3}{8}$

iii) Probability that a number is multiple of $3$

The multiples of 3 are: $33,39,57,75,93,99$

The probability that a number is multiple of $3$ is,

$P(multiple\ of\ 3)=\frac{6}{16}$

$P(multiple\ of\ 3)=\frac{3}{8}$