Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Probability question

2017 · 8 Apr · Shift 1 · Q38
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Probability
  5. /2017 · 8 Apr · Shift 1 · Q38

Probability question

2017 · 8 Apr · Shift 1 · Q38

JEE MainMathematicsProbabilityMCQ+4 / −1
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
  1. A
    255256{{255} \over {256}}256255​
  2. B
    127128{{127} \over {128}}128127​
  3. C
    6364{{63} \over {64}}6463​
  4. D
    12{{1} \over {2}}21​
View written solutionFree

Correct answer: B

  1. Total number of outcomes

    Since an unbiased coin is tossed 888 times, each toss has 222 possible outcomes.

    Hence total outcomes: 28=2562^8 = 25628=256

  2. Required event

    We need the probability of getting at least one head and at least one tail.

    This means we exclude only these two cases:

    • all heads
    • all tails

  3. Count unfavorable outcomes

    • All heads: 111 outcome
    • All tails: 111 outcome

    So total unfavorable outcomes: 1+1=21+1=21+1=2

  4. Count favorable outcomes

    256−2=254256-2=254256−2=254

  5. Compute probability

    P(at least one head and at least one tail)=254256=127128P(\text{at least one head and at least one tail}) = \frac{254}{256} = \frac{127}{128}P(at least one head and at least one tail)=256254​=128127​

  6. Option matching

    127128\frac{127}{128}128127​ corresponds to Option B.

Therefore, the correct answer is B.

PreviousNext

More from Probability

  • Let E and F be two independent events. The probability that both E and F happen is 121​ and the probability that neither E nor F happens is 21​, then a value of P(F)P(E)​ is…2017 · MCQ
  • From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :2017 · MCQ
  • If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :2017 · MCQ
  • For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = 41​ and P(All the three events occur simultaneously) =161​. Then the probability that…2017 · MCQ
  • If A and B are any two events such that P(A) = 52​ and P (A ∩ B) =203​, hen the conditional probability, P(A ∣(A' ∪ B')), where A' denotes the complement of A, is equal to :2016 · MCQ
  • Let two fair six-faced dice A and B be thrown simultaneously. If E1​ is the event that die A shows up four, E2​ is the event that die B shows up two and E3​ is the event that the sum of numbers on both dice is odd, then…2016 · MCQ
  • If 12 different balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :2015 · MCQ
  • Let A and B be two events such that P(A∪B)=61​,P(A∩B)=41​ and P(A)=41​, where A stands for the…2014 · MCQ