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Six letters are arranged in different sequences and each permutation has equal probability. The letters are: one S, one T, one C, one R, and two E’s. What is the probability that the sequence SECRET will occur?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

A box contains 10 light bulbs of which 3 are defective and 7 are not. An inspector randomly samples 3 bulbs without replacement Let X= the number of defective bulbs selected 

a. Construct the probability distribution of a.

b. What is the probability that at least one defective is selected?

c. What is the probability that the sample will contain at least one good buib?

People enter a restaurant and check their hat at the coat check, but since the worker is new, he makes the mistake of throwing all the hats in a pile. When the patrons return to claim their hats at the end of the evening, the worker gives each person a random hat from the pile.  

1. What is the probability that no one receives their own hat back if there are only 2guests?

2. What is the probability that no one receives their own hat back if there are 3 guests?

3. What is the probability that no one receives their own hat back if there are 4 guests?

4. What is the probability that no one receives their own hat back if there are 8 guests?

5.What is the probability that no one receives their own hat back if there are 10 guests?

To solve, build a systematic method. For example, one way you could do it is by defining several events, where P_i = the number of ways of a person i to recive their hat correctly, and then the number of ways that at least one person to recive their hat is the union of P_1,...,P_n; finally, you can count this using inclusion/exlusion, then count the complement to finish the problem. 

 

ou draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

No. The probability of drawing a specific second card depends on the identity of the first card.

No. The events cannot occur together.

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Yes. The events can occur together.

(b) Find P(3 on 1st card and 10 on 2nd). (Enter your answer as a fraction.)

(c) Find P(10 on 1st card and 3 on 2nd). (Enter your answer as a fraction.)

(d) Find the probability of drawing a 10 and a 3 in either order. (Enter your answer as a fraction.)

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