Question

Each letter of the word PROBABLE is written on a separate card. The cards are placed face down and mixed up. What is the probability that a randomly selected card has a VOWEL?

Answer 1

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✺Answer

♦️GiveN:

• Letters of the word PROBABLE are written in each of separate cards.
• Then, randomly some cards are selected.

♦️To FinD:

• Probability of choosing a vowel.

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✺Explanation Of Q.

In this above question, we have a word PROBABLE. The word contains 8 letters that are : P, R, O, B, A, B, L, E. These letters were written in 8 cards. Now, randomly we have to choose a card from it. Now, we have to find probability of selected card to be a Vowel.

Out of these lettes, the vowels are O, A, E

No. Of Vowels = 3

To find Probability, We need to know some basic concepts of Probability. Here is some basic concepts.

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✺We must know:

What is probability?

It refers to the happening or certanity of an element out of all possible outcomes is known as probability of that element.

It means, If there are n elementary events in a random experiment and no. of possible outcomes for E is m ,then probability of happening Of E is

$\large{ \boxed{ \rm{ \pink{P(E) = \frac{number \: of \: trials \: in \: which \: E \: can \: happen}{total \: number \: of \: possible \: outcomes \: }= \frac{m}{n} }}}}$

▶️ Point To Remember:

The Probability of happening of an event + probability of non happening is equals to 1.

$\large{ \boxed{ \rm{ P(E) + P\bar{(E)} = 1}}}$

Hence, we can conclude that

$\large{ \boxed{ \rm{\purple{0 \leqslant P(E) \leqslant 1}}}}$

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✺Solution:

No. of vowels = 3

So,No.of possible outcomes for a vowel = 3

Total no. of letters = 8

Total no. of possible outcomes= 8

So, By using The above formula,

$\large{ \rm{ \green{ \rightarrow \: P(vowel) = \boxed{ \frac{3}{8} }= \boxed{0.375} }}}$

♠️Hence, the probability of obtaining a vowel card out of all cards is 3/8 or 0.375.

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