Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Probability

BITSAT 2014 · Mathematics · Probability

A coin is tossed 7 times. Each time a man calls head. Find the...

A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

Options

  1. A23\frac{2}{3}
  2. B12\frac{1}{2}
  3. C34\frac{3}{4}
  4. D13\frac{1}{3}

Correct answer

B. 12\frac{1}{2}

Step-by-step solution

The man has to win at least 4 times. \begin{array}{r} \therefore\text{ Reqd. probability }=\\ \qquad \begin{array}{r}7 \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4} \cdot\left(\frac{1}{2}\right)^{3}+{ }^{7} \mathrm{C}_{5}\left(\frac{1}{2}\right)^{5} \cdot\left(\frac{1}{2}\right)^{2}\\ +{ }^{7} \mathrm{C}_{6}\left(\frac{1}{2}\right)^{6} \cdot \frac{1}{2}+{ }^{7} \mathrm{C}_{7}\left(\frac{1}{2}\right)^{7}\\ =\left({ }^{7} \mathrm{C}_{4}+{ }^{7} \mathrm{C}_{5}+{ }^{7} \mathrm{C}_{6}+{ }^{7} \mathrm{C}_{7}\right) \cdot \frac{1}{2^{7}}=\frac{64}{2^{7}}=\frac{1}{2} \end{array} \end{array}$
Practice Probability on Quantrex Academy →

More from Probability

The probability of getting 10 in a single throw of three fair dice is BITSAT 2024In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is BITSAT 2024The probability that certain electronic component fails when first used is 0.10. If it… BITSAT 2024Given below is the distribution of a random variable X If α=P(X 2) , then α: β= BITSAT 2024A book contains 1000 pages. A page is chosen at random. The probability that the sum of… BITSAT 2024For two events A and B , if P(A)=P( A B )=(1)/(4) and P((B)/(A))=(1)/(2) , then which of… BITSAT 2024If A and B are mutually exclusive events and if P(B)=(1)/(3), P(A B)=(13)/(21) , then… BITSAT 2023A coin is tossed twice. Then, the probability that atleast one tail occurs is BITSAT 2023If E and F are events such that 0 < P(F) < 1 , then BITSAT 2023The probability of getting sum more than 7 when a pair of dice are thrown is: BITSAT 2023The probability that a card drawn from a pack of 52 cards will be a diamond or king is: BITSAT 2023Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball… BITSAT 2023If P(B)=(3)/(5), P(A B)=(1)/(2) and P(A B)=(4)/(5) , then P(A B)^ +P(A^ B)= BITSAT 2023A six faced die is a biased one. It is thrice more likely to show an odd numbers than… BITSAT 2022Girl students constitute 10 \% of I year and 5 \% of II year at Roorkee University.… BITSAT 2021The mean and variance of a random variable X having binomial distribution are 4 and 2… BITSAT 2021 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs