Town has two fire extinguishing engines functioning independently. The probability of availability of each engine, when needed, is 0.95. what is the probability that (i)Neither of them is available when needed? (ii)An engine is available when needed? (iii)Exactly one engine is available when needed?

A scientist has to make a decision on each of the two independent events I and II . Suppose the probability of error in making decision on event I is 0.02 and that on event II is 0.05 . Find the probability that the scientist will make the correct decision on (i) both events (ii) only one event

Find the probability that when a hand of 7 cards is dealt from a well-shuffled deck of 52 cards, it contains (i) all 4 kings (ii) exactly 3 kings (iii) at least 3 kings.

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5. and 7. what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

One of the ten available keys opens the door. If we try the keys one after another, then find the following (i) the probability that the door is opened in the first attemt. (ii) the probability tht the door is opened in the second attempt. (iii) the probability that the door is opened in the third attempt. (iv) the probability that the door is opened in the tenth attempt.

A ship is fitted with three engines E_1,E_2 and E_3 . The engines function independently of each other with respective probabilities 1/2, 1/4, and 1/4 . For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X_1, X_2 and X_3 denote, respectively, the events that the engines E_1, E_2 and E_3 are function. Which of the following is/are true? (a) P(X_1^c "|"X)=3/(16) (b) P (exactly two engines of the ship are functioning "|"X ) =7/8 (c) P(X"|"X_2)=5/6 (d) P(X"|"X_1)=7/(16)

An electric tea kettle has two heating coils. When one of the coils is switched on , boiling begins in 6 min . When the other coil is switched on , boiling begins in 8 min . In what time will the boiling begin if both coils are switched on simultaneously (i) in series and (ii) in parallel.

A carnot engine has efficiency of 50% when its sink is at 227^(@)C . What is the temperature of source

One in 9 ships is likely to be wrecked when they are set on a sail. When 6 ships are on sail, find the probability for i) atleast one will arrive safely ii) exactly three will arrive safely.

A bag contains twenty Rs. 5 coins, fifty Rs. 2 coins and thirty Rs. 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin : (iii) will neither be a Rs. 5 coin nor be a Rs. 1 coin ?

If 4-digits numbers greater than or equal to 5000 are randomly formed form the digits 0, 1, 3, 5 and 7 what is the probability of forming number divisible by 5 when i. the digits may be repeated. ii. the repetition of digits is not allowed.