The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).

Suppose the probability that a coin toss shows "head" is , where . The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

The probability of a resistor being defective is 0.02. there are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is ________.

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its color. The probability to get a red ball in the second draw is

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is __________.

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colors that the candidates could bring. The probability that a candidates comes with all 3 pens having the same colour is _______.

Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

Two coins R and S are tossed. The 4 joint events  have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n – 3) is

Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is _______.

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A box contains 4 white balls and 3 red balls, In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is

Assume for simplicity that N people, all born in April (a month of 30 days), are collected in a room.  Consider the event of at least two people in the room being born on the same date of the month, even if in different years. e.g. 1980 and 1985. What is the smallest N so that the probability of this event exceeds 0.5 ?        

A loaded dice has following probability distribution of occurrences

If three identical dice as the above are thrown, the probability of occurrence of values

1, 5 and 6 on the three dice is

Two fair dice are rolled and the sum r of the numbers turned is considered.

If P and Q are two random events, then the following is TRUE:

A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is: