Statistics and Probability Answers

Suppose all licence plates in a certain region have three letters and three digits. If a plate is chosen at random. What is the probability that all three letters and all the numbers on the plate Will be different?

If a child is given cards with A, C, D, G, O and T on them, what is the probability that he/she could spell DOG by the correct arrangement of 3 cards from 6?

An automatic teller machine requires that each customer enter a four-digit personal identification number (PIN) when he/she insert a bank card. If person finds a bank card and guesses at a PIN to use the card fraudulently.
(I) what is the probability that a person will succeed in guessing in one attempt?
(II) if the person knows that PIN Will not have any repeated, what the probability that the person will succeed in guessing in one attempt?

Employees of a certain firm receive annual reviews. In a certain department, 4 employees received excellent ratings, 15 received good ratings and 1 received marginal rating. If 3 employees in this department are randomly selected to complete a form for internal study of firm, find the probability that
(I)all 3 selected were excellent
(II)one of each category were selected

An insurance company receives 25 claims in a certain month. Company policy mandates that a random selection of 5 of these claims be thoroughly investigated.if two of the 25 claims are fraudulent, find the probability that
(I)both claims are through investigated
(II) neither fraudulent claim is investigated

A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen from a group of 23 men and 19 women, find the probability that the subcommittee consists of
(I)6 men and 5 women
(II)all women

John noticed that his director is happy on 60% of his calls,so he assign a probability of his being happy on his visit as 0.6. he also noticed that if he is happy, he accedes to his request with a probability of 0.4 where as if he is not happy he accedes to the request with probability of 0.1. John called one day and the director accedes to john&'s request. What is the probability that is was happy?

A self administered pregnancy test detects 85% of those who are pregnant but does not detect pregnancy in 15%. It is 90% accurate in indicating a woman Who are not pregnant but indicates 10% of this group as being pregnant. Suppose it is known that 1% of the woman in a neighborhood are pregnant. if women is chosen at random from those living in this neighborhood, and if the test indicates that she is pregnant, what is the probability that she is really is?

The probability that an individual without college education earns more than $30000 is 0.2, where as the probability that a person with B.S. or higher degree earns $30000 is 0.6. the probability that a person chosen at random has B.S. degree is 0.3. what is the probability that a person has atleast a B.S. degree if it is known that he/she earns more than $30000?.

Suppose a box contains 3 defective transistors and 12 good transistors.if two transistors are drawn from the box without replacement what is the probability that.
(I)the first is good and second transistor is defective?
(II)the first transistor is defective and the second transistor is good?
(III)one of the drawn transistor is good and the other is defective?.