Question

What is the probability of drawing a valve out of a bag containing all the letters in the alphabet

Answer 1

Definition of probability says the probability of certain event is ratio of number of desired outcomes of an experience to the number of possible outcomes of that experiment (if they are equiprobable).

Number of letters in the alphabet = 26

for the letter VALVE

There is one V, A, L, E in the set of aplhabet

So

`\begin{gathered} \text{ Probability of letter V = }\frac{Number\text{ of V letters}}{Total\text{ number of letters}} \\ \text{ Probability of letter V =}(1)/(26) \\ \\ \text{ Probability of letter A = }\frac{Number\text{ of A letters}}{Total\text{ number of letters}} \\ \text{ Probability of letter A = }(1)/(26) \\ \\ \text{ Probability of letter L= }\frac{Number\text{ of L letters}}{Total\text{ number of letters}} \\ \text{ Probability of letter L = }(1)/(26) \\ \\ \text{ Probability of letter E = }\frac{Number\text{ of E letters}}{Total\text{ number of letters}} \\ \text{ Probability of letter E = }(1)/(26) \end{gathered}`

For the propbability of letter VALVE

So, substitute the value:

`\begin{gathered} \text{ Probability of Valve= }(1)/(26)+(1)/(26)+(1)/(26)+(1)/(26)+(1)/(26) \\ \text{Probability of Valve=}(5)/(26) \\ \text{Probability of Valve=}0.19 \end{gathered}`

Answer : 0.19