Question

What is the probability that , when Alex selects a positive even integer less than twenty and bob picks a positive multiple of 3 less than thirty, they pick the same number?
a) 1/3
b) 1/9
c) 2/27
d) 1/5

Answer 1

Step-by-step explanation:

• When Alex selects a positive even integer less than 20, it must be 2,4,6,8,10,12,14,16,18
• When Bob picks a positive multiple of 3 less than thirty, it must be 3,6,9,12,15,18,21,24,27

Let's form the cases first:-

• Divisible by 3 from the list of even integer:-
• 6,12,18

• Total number of cases formed :-
• 15 [ Don't count a number 2 times ]

Out of which:-

• Favorable outcomes :- 3 [6,12,18]

$\sf{Required \ Probability = \dfrac{Favourable \ Outcome}{Total \ Outcome}}$

$\sf{Required \ Probability = \dfrac{3}{15}}$

Simplifying:-

$\sf{Required \ Probability = \dfrac{1}{5}}$

Hence, d) part is the answer.

Answer 2

$\Large{\bf{Given\::}}$

• Alex selects a positive even integer less than 20.

• Bob picks a positive multiple of 3 less than 30.

• And they both pick the same number.

$\\ \Large{\bf{To\: Find\::}}$

• The probability of given case.

$\\ \Large{\bf{Solution\::}}$

➣ Alex selects a positive even integer less than 20.

Thus,

Favourable outcomes are,

➠ 2, 4, 6, 8, 10, 12, 14, 16, 18

Again,

➣ Bob picks a positive multiple of 3 less than 30.

Thus,

Favourable outcomes are,

➠ 3, 6, 9, 12, 15, 18, 21, 24, 27

Hence,

Total possible outcomes are,

➠ 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 24, 27

Therefore,

➠ Total no. of possible outcomes = 15

According to the question,

➣ They both pick the same number.

So,

The favourable outcomes are,

➠ 6, 12, 18

Therefore,

➠ Total no. of favourable outcomes = 3

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Probability\:=\:\dfrac{Total\:no.\:of\: favourable\: outcomes}{Total\:no.\:of\: possible\:outcomes}\:}\:{\Large\mid}\:\green\bigstar$

➠ Probability = $\tt{\dfrac{3}{15}}$

➠ Probability = $\bf\pink{\dfrac{1}{5}}$