A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of the red ball, find the number of blue balls in the bag.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We are given the number of red balls, and we have to find the number of blue balls. The number of red balls = 5
Let the number of blue balls in the bag be 𝑥.
So, the total number of balls in the bag = 5 + 𝑥
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑎𝑔
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑎𝑔
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙 = $\frac{n u m b e r o f r e d b a l l s i n t h e b a g}{t o t a l n u m b e r o f b a l l s i n t h e b a g}$
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙 = $\frac{5}{5 + x}$

⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑏𝑙𝑢𝑒 𝑏𝑎𝑙𝑙 = $\frac{n u m b e r o f b l u e b a l l s i n t h e b a g}{t o t a l n u m b e r o f b a l l s i n t h e b a g}$

⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑏𝑙𝑢𝑒 𝑏𝑎𝑙𝑙 = $\frac{x}{5 + x}$
According to the question,
Probability of drawing a blue ball from the bag = 3 × Probability of drawing a red ball Putting the values of probability, we get
$\frac{x}{5 + x}$ = 3 × $\frac{5}{5 + x}$

$\frac{x}{5 + x}$ = $\frac{15}{5 + x}$
As the denominator in both sides of the equation has the same denominator, i.e., 5 + 𝑥, the denominators will be cancelled. Then the equation becomes
𝑥 = 15
Hence, the number of blue balls is 15.

Watch 3-min video & get full concept clarity