Question

A die is tossed. What is the probability of getting:
(a) A number 5?
(b) A prime number?
(c) A number between 2 & 5?
(d) A number divisible by 6?

Answer 1

Answer:

a) 1/6

b) 1/2

c) 1/3

d) 0

Solution:

In all the sub-parts we will be solving, we will using the main formula to find the probability that will never change.

Formula:

$\sf{\boxed{Probability=\dfrac{Req.\:outcomes}{Total\:outcomes}}}$

Part A:

The number 5

Total no. of outcomes when a die is thrown = 6

Required outcome = 1

$\sf{Probability=\dfrac{Req.\:outcomes}{Total\:outcomes}}$

$\sf{Probability=\dfrac{1}{6}}$

The fraction is in the simplest form.

Hence the required answer is 1/6.

Part B:

A prime number

Total no. of outcomes when a die is thrown = 6

Required outcome = the prime numbers between 1 and 6 [2,3 and 5] = 3

$\sf{Probability=\dfrac{Req.\:outcomes}{Total\:outcomes}}$

$\sf{Probability=\dfrac{3}{6}}$

The fraction 3/6 can be reduced to 1/2 by dividing both the numerator and denominator with 3.

Hence the required answer is 1/2.

Part C:

A number between 2 and 5

Total no. of outcomes when a die is thrown = 6

Required outcome = numbers between 2 and 5 [3 and 4] = 2

$\sf{Probability=\dfrac{Req.\:outcomes}{Total\:outcomes}}$

$\sf{Probability=\dfrac{2}{6}}$

The fraction 2/6 can be reduced to 1/3 by dividing both the numerator and denominator with 2.

Hence the required answer is 1/3.

Part D:

A number divisible by 6

The numbers on the dice are from 1 to 6 and hence there is no number that is divisible by 6.

Hence the required answer is 0.