Explanation

• The formula for probability is: Favorable Outcomes ÷ Total Outcomes.
• Probability measures the chance of an event occurring.
• Its value always lies between 0 and 1.
• 0 means the event is impossible, while 1 means it is certain.
• It is widely used in mathematics, statistics, and everyday decision-making.

Last verified on 12-07-2026

Explanation

Total number of machines = 140  

Number of defective machines = 30  

Probability = Number of defective machines / Total number of machines  

Probability = 30 / 140  

Probability = 3 / 14  

Last verified on 11-07-2026

Explanation

Total balls = 4 blue + 3 red = 7  

Number of red balls = 3  

Probability = Favorable outcomes / Total outcomes  

= Number of red balls / Total balls  

= 3 / 7

Last verified on 11-07-2026

Explanation

n = 5 questions  

k = 2 correct  

p = 1/5 = 0.2 probability correct  

q = 4/5 = 0.8 probability wrong  

Formula: P = C(n,k) _ p^k _ q^(n-k)  

P = C(5,2) _ (0.2)^2 _ (0.8)^3  

P = 10 _ 0.04 _ 0.512  

P = 0.2048  

So probability of getting exactly 2 correct = 0.2048 = 128/625 (20.48%)

Last verified on 11-07-2026

Explanation

For n people sitting around a circular table:

Number of arrangements = (n − 1)!

For 10 people:

(10 − 1)! = 9! = 362,880

Last verified on 11-07-2026