Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202525 Apr 2025Evening ShiftMathematicsProbabilityActual

A player tosses two coins. He wins Rs. 10, if 2 heads appears, Rs. 5, if one head appear and Rs. 2 if no head appears. Then variance of winning amount is

Options

  1. A38.5
  2. B5.5
  3. C8.25
  4. D44.00

Correct answer

C. 8.25

Step-by-step solution

Expected value and variance for the two-coin toss game In a game where two fair coins are tossed, the possible outcomes are HH , HT , TH , and TT , each with probability 1 4 . The winning amount X is 10 for HH ( P(X=10)=1/4 ), 5 for HT or TH ( P(X=5)=1/2 ), and 2 for TT ( P(X=2)=1/4 ). The expected value is E(X) = x P(X=x) = 10 1 4 + 5 1 2 + 2 1 4 = 5.5 . E(X^2) = 100 1 4 + 25 1 2 + 4 1 4 = 38.5 . Variance is Var (X) = E(X^2) - [E(X)]^2 = 38.5 - (5.5)^2 = 8.25 . Hence, the variance is C .

Practice Probability on Quantrex Academy →

More from Probability

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is 1 4 and the probability that the second student g 2025For three events A, B and C of a sample space, P(exactly one of A or B occurs)= P ( exactly one of B or C occurs )= P ( exactly one of C or A occurs )= 1 4 . If probability of all 2025A bag P contains 4 red and 5 black balls, another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag P and two balls are drawn from bag Q, then the pro 2025On every evening, a student either watches TV or reads a book. The probability of watching TV is 4 5 . If he watches TV, the probability that he will fall asleep is 3 4 and it is 1 2025Let X be the random variable taking values 1,2, , n for a fixed positive integer n. If P ( X = k )= 1 n for 1 k n , then the variance of X is 2025A radar system can detect an enemy plane in one out of ten consecutive scans. The probability that it can detect an enemy plane atleast twice in four consecutive scans is 2025Three numbers are chosen from 1 to 30. The probability that they are not three consecutive numbers is 2025If two events A and B are such that P ( A )=0.3, P ( B )=0.4 and P ( A B )=0.5 , then P ( B /( A B ))= 2025 Full Probability list All MHT CET PYQs