From six letters a, b, c, d, e, and f, three letters are choosen at random with replacement. What is the probability that the word bad or cad can be formed from the choosen letter?
Answers
The letters are chosen with replacement. So each time there are 6 letters to choose from.
The word bad/ cad can be formed if the three letters in that word are picked in the three picks.
Probability of choosing ' c' or 'b' = 2/6 = 1/3.
Probability of choosing 'a' = 1/6
Probability of choosing ' b' = 1/6
These three picking events are independent.
The order of getting them doesn't matter. So 3 ! = 6 permutations are possible.
Overall probability = 6 × 1/3 × 1/6 × 1/6
= 1/18.
Answer:
Explanation:
The letters are selected with substitution. There are so six letters available each time.
If the three letters that make up that word are chosen from the three choices, the word bad/cad can be created.
The likelihood of selecting "c" or "b" is 2/6, or 1/3.
The likelihood of selecting "a" is 1/6.
The likelihood of selecting "b" is 1/6.
Each of these three picking incidents is separate.
It doesn't matter in what sequence you obtain them. There can therefore be 3! = 6 permutations.
Probability overall = 6 1/3 1/6 1/6
= 1/18.
Therefore the overall probability to form the words "bad" and "cad" will be 1/18.
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